Question 1

Sketch the curves without any technological help.   $f ( t ) = \cos t$ ; $g ( t ) = \cos ( t + \pi )$

Accepted Answer

A)     
B)      
C)      
D)      
E)     
A)     
B)      
C)      
D)      
E)

Question 2

Find the derivative of the function.   $f ( x ) = 9 \sin x - 8 \cos x$

Accepted Answer

A)  $f ^ { \prime } ( x ) = 9 \cos x + 8 \sin x$ 
B)  $f ^ { \prime } ( x ) = 8 \cos x - 9 \sin x$ 
C)    $f ^ { \prime } ( x ) = 9 \cos x - 8 \sin x$ 
D)  $f ^ { \prime } ( x ) = - 9 \cos x - 8 \sin x$ 
E)  $f ^ { \prime } ( x ) = 8 \cos x + 9 \sin x$ 
A)  $f ^ { \prime } ( x ) = 9 \cos x + 8 \sin x$ 
B)  $f ^ { \prime } ( x ) = 8 \cos x - 9 \sin x$ 
C)    $f ^ { \prime } ( x ) = 9 \cos x - 8 \sin x$ 
D)  $f ^ { \prime } ( x ) = - 9 \cos x - 8 \sin x$ 
E)  $f ^ { \prime } ( x ) = 8 \cos x + 9 \sin x$

Question 3

Use the conversion formula $\cos x = \sin \left( \frac { \pi } { 2 } - x \right)$ to replace the expression   $f ( t ) = 5.2 \cos ( 6 \pi t ) + 10$  
By a sine function.

Accepted Answer

A)  $f ( t ) = 5.2 \sin \left( \frac { \pi } { 2 } - 6 \pi t \right) + 10$ 
B)  $f ( t ) = 5.2 \sin \left( \frac { \pi - 6 \pi t } { 2 } \right) + 10$ 
C)  $f ( t ) = 5.2 \sin \left( \frac { \pi } { 2 } - 6 t \right) + 10$ 
D)  $f ( t ) = 6 \sin \left( \frac { \pi } { 2 } - 5.2 \pi t \right) + 10$ 
E)  $f ( t ) = 10 \sin \left( \frac { \pi } { 2 } - 6 \pi t \right) + 5.2$ 
A)  $f ( t ) = 5.2 \sin \left( \frac { \pi } { 2 } - 6 \pi t \right) + 10$ 
B)  $f ( t ) = 5.2 \sin \left( \frac { \pi - 6 \pi t } { 2 } \right) + 10$ 
C)  $f ( t ) = 5.2 \sin \left( \frac { \pi } { 2 } - 6 t \right) + 10$ 
D)  $f ( t ) = 6 \sin \left( \frac { \pi } { 2 } - 5.2 \pi t \right) + 10$ 
E)  $f ( t ) = 10 \sin \left( \frac { \pi } { 2 } - 6 \pi t \right) + 5.2$

Question 4

Find the derivative of the function.  $s ( x ) = \left( 4 x ^ { 2 } - 2 x + 2 \right) \tan x$

Accepted Answer

A)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } - 2 x - 2 \right) \sec ^ { 2 } x$ 
B)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } - 2 x + 2 \right) \sec x$ 
C)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } + 2 x + 2 \right) \sec ^ { 2 } x$ 
D)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } - 2 x + 2 \right) \sec ^ { 2 } x$ 
E)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x - \left( 4 x ^ { 2 } - 2 x + 2 \right) \sec ^ { 2 } x$ 
A)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } - 2 x - 2 \right) \sec ^ { 2 } x$ 
B)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } - 2 x + 2 \right) \sec x$ 
C)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } + 2 x + 2 \right) \sec ^ { 2 } x$ 
D)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x + \left( 4 x ^ { 2 } - 2 x + 2 \right) \sec ^ { 2 } x$ 
E)  $s ^ { \prime } ( x ) = ( 8 x - 2 ) \tan x - \left( 4 x ^ { 2 } - 2 x + 2 \right) \sec ^ { 2 } x$

Question 5

Use geometry to compute the given integral.  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x$

Accepted Answer

A)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 5$ 
B)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 12$ 
C)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 1$ 
D)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 0$ 
E)  none of these 
A)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 5$ 
B)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 12$ 
C)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 1$ 
D)  $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x = 0$ 
E)  none of these

Question 6

Recall that the total income received from time $t = a$ to time $t = b$ from a continuous income stream of $R ( t )$ dollars per year is  
Total value = TV = $\int _ { a } ^ { b } R ( t ) \mathrm { d } t$  
Find the total value of the given income stream and also find its future value (at the end of the given interval) using the given interest rate.
  $R ( t ) = 800,000 \sin ( 2 \pi t )$ , $0 \leq t \leq 5$ , at 9%

Accepted Answer

A) TV = $0, FV = $72,344.91 
B)  TV = $0, FV = $327,074.77 
C)  TV = $1,600,000, FV = $834,722.23 
D)  TV = $0, FV = $256,372.45 
E)  none of these 
A) TV = $0, FV = $72,344.91 
B)  TV = $0, FV = $327,074.77 
C)  TV = $1,600,000, FV = $834,722.23 
D)  TV = $0, FV = $256,372.45 
E)  none of these

Question 7

Model the curve with a sine function.     
Note that the period of the curve is $P = 32$ and its range is $[ - 40,0 ]$ , the graph of the sine function is shifted to the right 7 units.

Accepted Answer

A)  $f ( x ) = 20 \sin \left( \frac { \pi ( x + 7 ) } { 16 } \right) + 20$ 
B)  $f ( x ) = - 20 \sin \left( \frac { \pi ( x + 7 ) } { 16 } \right) + 20$ 
C)  $f ( x ) = 40 \sin \left( \frac { \pi ( x - 7 ) } { 16 } \right) - 40$ 
D)  $f ( x ) = 40 \sin \left( \frac { \pi ( x + 7 ) } { 16 } \right) - 40$ 
E)  $f ( x ) = 20 \sin \left( \frac { \pi ( x - 7 ) } { 16 } \right) - 20$ 
A)  $f ( x ) = 20 \sin \left( \frac { \pi ( x + 7 ) } { 16 } \right) + 20$ 
B)  $f ( x ) = - 20 \sin \left( \frac { \pi ( x + 7 ) } { 16 } \right) + 20$ 
C)  $f ( x ) = 40 \sin \left( \frac { \pi ( x - 7 ) } { 16 } \right) - 40$ 
D)  $f ( x ) = 40 \sin \left( \frac { \pi ( x + 7 ) } { 16 } \right) - 40$ 
E)  $f ( x ) = 20 \sin \left( \frac { \pi ( x - 7 ) } { 16 } \right) - 20$

Question 8

Evaluate the integral. ? $\int ( 8 \cos x - 4.1 \sin x - 9.3 ) \mathrm { d } x$ ?

Accepted Answer

A)  $8 \sin x + 4.1 \cos x - 9.3 x + C$ 
B)  $- 8 \sin x + 4.1 \cos x + C$ 
C)  $8 \sin x - 4.1 \cos x - 9.3 x + C$ 
D)  $- 8 \sin x - 4.1 \cos x + C$ 
E)  $8 \sin x - 4.1 \cos x + 9.3 x + C$ 
A)  $8 \sin x + 4.1 \cos x - 9.3 x + C$ 
B)  $- 8 \sin x + 4.1 \cos x + C$ 
C)  $8 \sin x - 4.1 \cos x - 9.3 x + C$ 
D)  $- 8 \sin x - 4.1 \cos x + C$ 
E)  $8 \sin x - 4.1 \cos x + 9.3 x + C$

Question 9

Evaluate the integral.
​ $\int 8.4 \cos ( 4 x - 2 ) \mathrm { d } x$ ​
Use the symbol C to write the constant.

Accepted Answer

The answer of Evaluate the integral.
​ \(\int 8.4 \cos (...

Question 10

Find the derivative of the function.   $u ( x ) = \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right)$

Accepted Answer

A)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } + 2.8 \right) \sec \left( x ^ { 5.2 } - 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } - 2.8 x - 9 \right)$ 
B)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } - 2.8 \right) \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } + 2.8 x - 9 \right)$ 
C)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } - 2.8 \right) \sec \left( x ^ { 5.2 } - 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } + 2.8 x - 9 \right)$ 
D)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } + 2.8 \right) \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } + 2.8 x - 9 \right)$ 
E)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } - 2.8 \right) \sec \left( x ^ { 5.2 } - 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } - 2.8 x - 9 \right)$ 
A)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } + 2.8 \right) \sec \left( x ^ { 5.2 } - 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } - 2.8 x - 9 \right)$ 
B)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } - 2.8 \right) \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } + 2.8 x - 9 \right)$ 
C)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } - 2.8 \right) \sec \left( x ^ { 5.2 } - 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } + 2.8 x - 9 \right)$ 
D)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } + 2.8 \right) \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } + 2.8 x - 9 \right)$ 
E)  $u ^ { \prime } ( x ) = \left( 5.2 x ^ { 4.2 } - 2.8 \right) \sec \left( x ^ { 5.2 } - 2.8 x - 9 \right) \tan \left( x ^ { 5.2 } - 2.8 x - 9 \right)$

Question 11

The depth of water $d ( t )$ at my favorite surfing spot varies from 8 to 20 feet, depending on the time. Last Sunday high tide occurred at 5:00 A.M. and the next high tide occurred at 6:30 P.M. Use a sine function to model the depth of water as a function of time t in hours since midnight on Sunday morning.

Accepted Answer

A)  $d ( t ) = 10 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 4$ 
B)  $d ( t ) = 6 \sin \left( \frac { 2 \pi ( t + 1.625 ) } { 11.5 } \right) - 14$ 
C)  $d ( t ) = - 6 \sin \left( \frac { - 2 \pi ( t + 1.625 ) } { 13.5 } \right) + 14$ 
D)  $d ( t ) = 6 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 14$ 
E)  $d ( t ) = 14 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 6$ 
A)  $d ( t ) = 10 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 4$ 
B)  $d ( t ) = 6 \sin \left( \frac { 2 \pi ( t + 1.625 ) } { 11.5 } \right) - 14$ 
C)  $d ( t ) = - 6 \sin \left( \frac { - 2 \pi ( t + 1.625 ) } { 13.5 } \right) + 14$ 
D)  $d ( t ) = 6 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 14$ 
E)  $d ( t ) = 14 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 6$

Question 12

Model the curve with a sine function.    
Note that the period of the curve is $P = 0.4$ and its range is $[ - 3 , - 1 ]$ .

Accepted Answer

A)  $f ( x ) = 2 - \sin x$ 
B)  $f ( x ) = - 2 + 5 \sin x$ 
C)   $f ( x ) = - 2 + \sin ( 5 \pi x )$ 
D)  $f ( x ) = 2 - \sin ( 5 \pi x )$ 
E)  $f ( x ) = - 2 + \sin ( \pi x )$ 
A)  $f ( x ) = 2 - \sin x$ 
B)  $f ( x ) = - 2 + 5 \sin x$ 
C)   $f ( x ) = - 2 + \sin ( 5 \pi x )$ 
D)  $f ( x ) = 2 - \sin ( 5 \pi x )$ 
E)  $f ( x ) = - 2 + \sin ( \pi x )$

Question 13

Decide whether each integral converges. If the integral converges, compute its value.
Choose the correct letter for each question.

-converges to $\frac { 1 } { 4 }$

Accepted Answer

A) $\int _ { 0 } ^ { + \infty } \sin ( 2 x ) \mathrm { d } x$ 
B) $\int _ { 0 } ^ { + \infty } e ^ { - 2 x } \sin ( 2 x ) \mathrm { d } x$ 
A) $\int _ { 0 } ^ { + \infty } \sin ( 2 x ) \mathrm { d } x$ 
B) $\int _ { 0 } ^ { + \infty } e ^ { - 2 x } \sin ( 2 x ) \mathrm { d } x$

Question 14

Calculate the derivative.  $\frac { d } { d x } [ \sin ( 7 x ) ] ^ { 0.5 }$

Accepted Answer

A)  $3.5 \sin ( 7 x ) \cdot \cos ( 7 x )$ 
B)  $3.5 ( \sin ( 7 x ) ) ^ { - 0.5 } \cdot \cos ( 7 x )$ 
C)  $( \sin ( 7 x ) ) ^ { - 0.5 } \cdot \cos ( 7 x )$ 
D)  $7 ( \sin ( 7 x ) ) ^ { - 0.5 } \cdot \cos ( 7 x )$ 
E)  $7 ( \sin ( 7 x ) ) ^ { 0.5 } \cdot \cos ( 7 x )$ 
A)  $3.5 \sin ( 7 x ) \cdot \cos ( 7 x )$ 
B)  $3.5 ( \sin ( 7 x ) ) ^ { - 0.5 } \cdot \cos ( 7 x )$ 
C)  $( \sin ( 7 x ) ) ^ { - 0.5 } \cdot \cos ( 7 x )$ 
D)  $7 ( \sin ( 7 x ) ) ^ { - 0.5 } \cdot \cos ( 7 x )$ 
E)  $7 ( \sin ( 7 x ) ) ^ { 0.5 } \cdot \cos ( 7 x )$

Question 15

Use the formula for $\sin ( x + y )$ to simplify the expression $\sin \left( t + \frac { 17 \pi } { 2 } \right)$ .

Accepted Answer

A)  $\cos t - 17 \pi$ 
B)  $\cos t + 17 \pi$ 
C)  $\frac { \cos t } { 17 \pi }$ 
D)  $17 \pi \cos t$ 
E)  $\cos t$ 
A)  $\cos t - 17 \pi$ 
B)  $\cos t + 17 \pi$ 
C)  $\frac { \cos t } { 17 \pi }$ 
D)  $17 \pi \cos t$ 
E)  $\cos t$

Question 16

Model the curve with a cosine function.     
Note that the period of the curve is $P = \frac { 1 } { 6 }$ and its range is $[ - 1,1 ]$ .

Accepted Answer

A)  $f ( x ) = \cos ( 12 x )$ 
B)  $f ( x ) = \cos \left( \frac { \pi x } { 12 } \right)$ 
C)  $f ( x ) = \cos ( 12 \pi x )$ 
D)  $f ( x ) = 12 \cos ( \pi x )$ 
E)  $f ( x ) = \cos \left( \frac { x } { 12 } \right)$ 
A)  $f ( x ) = \cos ( 12 x )$ 
B)  $f ( x ) = \cos \left( \frac { \pi x } { 12 } \right)$ 
C)  $f ( x ) = \cos ( 12 \pi x )$ 
D)  $f ( x ) = 12 \cos ( \pi x )$ 
E)  $f ( x ) = \cos \left( \frac { x } { 12 } \right)$

Question 17

Find the derivative of the function.   $y ( x ) = \sec \left( e ^ { 4 x } \right)$

Accepted Answer

A)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$ 
B)  $y ^ { \prime } ( x ) = 16 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$ 
C)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$ 
D)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc ^ { 2 } \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$ 
E)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$ 
A)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$ 
B)  $y ^ { \prime } ( x ) = 16 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$ 
C)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$ 
D)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc ^ { 2 } \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$ 
E)  $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$

Question 18

Use the addition formulas: $$\begin{array} { l } 
\sin ( x + y ) = \sin x \cdot \cos y + \cos x \cdot \sin y \
\sin ( x - y ) = \sin x \cdot \cos y - \cos x \cdot \sin y \
\cos ( x + y ) = \cos x \cdot \cos y - \sin x \cdot \sin y \
\cos ( x - y ) = \cos x \cdot \cos y + \sin x \cdot \sin y
\end{array}$$  
To express $\tan ( x + 23 \pi )$ in terms of $\tan ( x )$ .

Accepted Answer

A)  $\frac { \tan ( x ) } { 23 \pi }$ 
B)  $\tan ( x ) + 23 \pi$ 
C)  $23 \pi \tan ( x )$ 
D)  $\tan ( x )$ 
E)  $\tan ( x ) - 23 \pi$ 
A)  $\frac { \tan ( x ) } { 23 \pi }$ 
B)  $\tan ( x ) + 23 \pi$ 
C)  $23 \pi \tan ( x )$ 
D)  $\tan ( x )$ 
E)  $\tan ( x ) - 23 \pi$

Question 19

Evaluate the integral.
​ $\int \left( x ^ { 2 } + x ^ { 4 } \right) \sec ^ { 2 } \left( 5 x ^ { 3 } + 3 x ^ { 5 } \right) \mathrm { dx }$ ​
Use the symbol C to write the constant.

Accepted Answer

The answer of Evaluate the integral.
​ \(\int \left( x ^...

Question 20

Find the derivative of the function.  $r ( x ) = 4 x \cos x + 9 x ^ { 2 } + 8$

Accepted Answer

A)  $r'( x ) = - 4 x \cos x + 4 \cos x + 18 x$ 
B)  $r' ( x ) = - 4 x \sin x + 4 \cos x + 18 x$ 
C)  $r '( x ) = - 4 x \sin x + 4 \cos x - 18 x$ 
D)  $r '( x ) = - 4 x \sin x + 4 \sin x + 18 x$ 
E)  $r '( x ) = 4 x \sin x - 4 \cos x + 18 x$ 
A)  $r'( x ) = - 4 x \cos x + 4 \cos x + 18 x$ 
B)  $r' ( x ) = - 4 x \sin x + 4 \cos x + 18 x$ 
C)  $r '( x ) = - 4 x \sin x + 4 \cos x - 18 x$ 
D)  $r '( x ) = - 4 x \sin x + 4 \sin x + 18 x$ 
E)  $r '( x ) = 4 x \sin x - 4 \cos x + 18 x$

Sketch the curves without any technological help. $f ( t ) = \cos t$ ; $g ( t ) = \cos ( t + \pi )$

Find the derivative of the function. $f ( x ) = 9 \sin x - 8 \cos x$

Use the conversion formula $\cos x = \sin \left( \frac { \pi } { 2 } - x \right)$ to replace the expression $f ( t ) = 5.2 \cos ( 6 \pi t ) + 10$ By a sine function.

Find the derivative of the function. $s ( x ) = \left( 4 x ^ { 2 } - 2 x + 2 \right) \tan x$

Use geometry to compute the given integral. $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x$

Model the curve with a sine function. Note that the period of the curve is $P = 32$ and its range is $[ - 40,0 ]$ , the graph of the sine function is shifted to the right 7 units.

Evaluate the integral. ? $\int ( 8 \cos x - 4.1 \sin x - 9.3 ) \mathrm { d } x$ ?

Evaluate the integral. $\int 8.4 \cos ( 4 x - 2 ) \mathrm { d } x$ Use the symbol C to write the constant.

Find the derivative of the function. $u ( x ) = \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right)$

Model the curve with a sine function. Note that the period of the curve is $P = 0.4$ and its range is $[ - 3 , - 1 ]$ .

Decide whether each integral converges. If the integral converges, compute its value. Choose the correct letter for each question. -converges to $\frac { 1 } { 4 }$

Calculate the derivative. $\frac { d } { d x } [ \sin ( 7 x ) ] ^ { 0.5 }$

Use the formula for $\sin ( x + y )$ to simplify the expression $\sin \left( t + \frac { 17 \pi } { 2 } \right)$ .

Model the curve with a cosine function. $Model the curve with a cosine function. Note that the period of the curve is P = \frac { 1 } { 6 } and its range is [ - 1,1 ] .$ Note that the period of the curve is $P = \frac { 1 } { 6 }$ and its range is $[ - 1,1 ]$ .

Find the derivative of the function. $y ( x ) = \sec \left( e ^ { 4 x } \right)$

Use the addition formulas: (x+y)=x\cdoty+x\cdoty (x-y)=x\cdoty-x\cdoty (x+y)=x\cdoty-x\cdoty (x-y)=x\cdoty+x\cdoty To express $\tan ( x + 23 \pi )$ in terms of $\tan ( x )$ .

Evaluate the integral. $\int \left( x ^ { 2 } + x ^ { 4 } \right) \sec ^ { 2 } \left( 5 x ^ { 3 } + 3 x ^ { 5 } \right) \mathrm { dx }$ Use the symbol C to write the constant.

Find the derivative of the function. $r ( x ) = 4 x \cos x + 9 x ^ { 2 } + 8$

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Exam 16: Trigonometric Models

Sketch the curves without any technological help. f(t)=cos⁡tf ( t ) = \cos tf(t)=cost ; g(t)=cos⁡(t+π)g ( t ) = \cos ( t + \pi )g(t)=cos(t+π)

Find the derivative of the function. f(x)=9sin⁡x−8cos⁡xf ( x ) = 9 \sin x - 8 \cos xf(x)=9sinx−8cosx

Use the conversion formula cos⁡x=sin⁡(π2−x)\cos x = \sin \left( \frac { \pi } { 2 } - x \right)cosx=sin(2π​−x) to replace the expression f(t)=5.2cos⁡(6πt)+10f ( t ) = 5.2 \cos ( 6 \pi t ) + 10f(t)=5.2cos(6πt)+10 By a sine function.

Find the derivative of the function. s(x)=(4x2−2x+2)tan⁡xs ( x ) = \left( 4 x ^ { 2 } - 2 x + 2 \right) \tan xs(x)=(4x2−2x+2)tanx

Use geometry to compute the given integral. ∫05π6cos⁡xdx\int _ { 0 } ^ { 5 \pi } 6 \cos x d x∫05π​6cosxdx

Model the curve with a sine function. Note that the period of the curve is P=32P = 32P=32 and its range is [−40,0][ - 40,0 ][−40,0] , the graph of the sine function is shifted to the right 7 units.

Evaluate the integral. ? ∫(8cos⁡x−4.1sin⁡x−9.3)dx\int ( 8 \cos x - 4.1 \sin x - 9.3 ) \mathrm { d } x∫(8cosx−4.1sinx−9.3)dx ?

Evaluate the integral. ​ ∫8.4cos⁡(4x−2)dx\int 8.4 \cos ( 4 x - 2 ) \mathrm { d } x∫8.4cos(4x−2)dx ​ Use the symbol C to write the constant.

Find the derivative of the function. u(x)=sec⁡(x5.2+2.8x−9)u ( x ) = \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right)u(x)=sec(x5.2+2.8x−9)

Model the curve with a sine function. Note that the period of the curve is P=0.4P = 0.4P=0.4 and its range is [−3,−1][ - 3 , - 1 ][−3,−1] .

Decide whether each integral converges. If the integral converges, compute its value. Choose the correct letter for each question. -converges to 14\frac { 1 } { 4 }41​

Calculate the derivative. ddx[sin⁡(7x)]0.5\frac { d } { d x } [ \sin ( 7 x ) ] ^ { 0.5 }dxd​[sin(7x)]0.5

Use the formula for sin⁡(x+y)\sin ( x + y )sin(x+y) to simplify the expression sin⁡(t+17π2)\sin \left( t + \frac { 17 \pi } { 2 } \right)sin(t+217π​) .

Model the curve with a cosine function. Note that the period of the curve is P=16P = \frac { 1 } { 6 }P=61​ and its range is [−1,1][ - 1,1 ][−1,1] .

Find the derivative of the function. y(x)=sec⁡(e4x)y ( x ) = \sec \left( e ^ { 4 x } \right)y(x)=sec(e4x)

Use the addition formulas: (x+y)=x\cdoty+x\cdoty (x-y)=x\cdoty-x\cdoty (x+y)=x\cdoty-x\cdoty (x-y)=x\cdoty+x\cdoty To express tan⁡(x+23π)\tan ( x + 23 \pi )tan(x+23π) in terms of tan⁡(x)\tan ( x )tan(x) .

Evaluate the integral. ​ ∫(x2+x4)sec⁡2(5x3+3x5)dx\int \left( x ^ { 2 } + x ^ { 4 } \right) \sec ^ { 2 } \left( 5 x ^ { 3 } + 3 x ^ { 5 } \right) \mathrm { dx }∫(x2+x4)sec2(5x3+3x5)dx ​ Use the symbol C to write the constant.

Find the derivative of the function. r(x)=4xcos⁡x+9x2+8r ( x ) = 4 x \cos x + 9 x ^ { 2 } + 8r(x)=4xcosx+9x2+8

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Sketch the curves without any technological help. $f ( t ) = \cos t$ ; $g ( t ) = \cos ( t + \pi )$

Find the derivative of the function. $f ( x ) = 9 \sin x - 8 \cos x$

Use the conversion formula $\cos x = \sin \left( \frac { \pi } { 2 } - x \right)$ to replace the expression $f ( t ) = 5.2 \cos ( 6 \pi t ) + 10$ By a sine function.

Find the derivative of the function. $s ( x ) = \left( 4 x ^ { 2 } - 2 x + 2 \right) \tan x$

Use geometry to compute the given integral. $\int _ { 0 } ^ { 5 \pi } 6 \cos x d x$

Model the curve with a sine function. Note that the period of the curve is $P = 32$ and its range is $[ - 40,0 ]$ , the graph of the sine function is shifted to the right 7 units.

Evaluate the integral. ? $\int ( 8 \cos x - 4.1 \sin x - 9.3 ) \mathrm { d } x$ ?

Evaluate the integral. $\int 8.4 \cos ( 4 x - 2 ) \mathrm { d } x$ Use the symbol C to write the constant.

Find the derivative of the function. $u ( x ) = \sec \left( x ^ { 5.2 } + 2.8 x - 9 \right)$

Model the curve with a sine function. Note that the period of the curve is $P = 0.4$ and its range is $[ - 3 , - 1 ]$ .

Decide whether each integral converges. If the integral converges, compute its value. Choose the correct letter for each question. -converges to $\frac { 1 } { 4 }$

Calculate the derivative. $\frac { d } { d x } [ \sin ( 7 x ) ] ^ { 0.5 }$

Use the formula for $\sin ( x + y )$ to simplify the expression $\sin \left( t + \frac { 17 \pi } { 2 } \right)$ .

Model the curve with a cosine function. $Model the curve with a cosine function. Note that the period of the curve is P = \frac { 1 } { 6 } and its range is [ - 1,1 ] .$ Note that the period of the curve is $P = \frac { 1 } { 6 }$ and its range is $[ - 1,1 ]$ .

Find the derivative of the function. $y ( x ) = \sec \left( e ^ { 4 x } \right)$

Use the addition formulas: (x+y)=x\cdoty+x\cdoty (x-y)=x\cdoty-x\cdoty (x+y)=x\cdoty-x\cdoty (x-y)=x\cdoty+x\cdoty To express $\tan ( x + 23 \pi )$ in terms of $\tan ( x )$ .

Evaluate the integral. $\int \left( x ^ { 2 } + x ^ { 4 } \right) \sec ^ { 2 } \left( 5 x ^ { 3 } + 3 x ^ { 5 } \right) \mathrm { dx }$ Use the symbol C to write the constant.

Find the derivative of the function. $r ( x ) = 4 x \cos x + 9 x ^ { 2 } + 8$