Question 1

Evaluate $\int _ { 2 } ^ { 10 } \frac { 1 } { ( 2 x + 5 ) \sqrt { ( 2 x + 5 ) } } d x$

Accepted Answer

A) 2,882 
B) 766 
C) 625 
D) 525.8 
E) 576.4 
A) 2,882 
B) 766 
C) 625 
D) 525.8 
E) 576.4 E

Question 2

Which of the following expressions represents the present value of a continuous revenue stream for n years at a constant rate of $S per year if the discount rate is r%?

Accepted Answer

A)  $\frac { r } { 100 S } \left[ e ^ { \frac { - m } { 100 } } + 1 \right]$ 
B)  $\frac { r S e ^ { \frac { - m } { 100 } } } { 100 }$ 
C)  $\frac { \boldsymbol { r } } { 100 S } \left[ e ^ { \frac { - \boldsymbol { m } } { 100 } } - 1 \right]$ 
D)  $\frac { 100 S e ^ { \frac { - m } { 100 } } } { r }$ 
E)  $\frac { 100 S } { r } \left[ 1 - e ^ { \frac { - m } { 100 } } \right]$ 
A)  $\frac { r } { 100 S } \left[ e ^ { \frac { - m } { 100 } } + 1 \right]$ 
B)  $\frac { r S e ^ { \frac { - m } { 100 } } } { 100 }$ 
C)  $\frac { \boldsymbol { r } } { 100 S } \left[ e ^ { \frac { - \boldsymbol { m } } { 100 } } - 1 \right]$ 
D)  $\frac { 100 S e ^ { \frac { - m } { 100 } } } { r }$ 
E)  $\frac { 100 S } { r } \left[ 1 - e ^ { \frac { - m } { 100 } } \right]$ E

Question 3

Find $\int x ^ { 3 } - \frac { 5 } { x ^ { 6 } } + \frac { 2 } { x } - 4 e ^ { - 4 x } d x$

Accepted Answer

A)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + \ln x ^ { 2 } + e ^ { - 4 x } + c$ 
B)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + 2 \ln x ^ { 2 } - e ^ { - 4 x } + c$ 
C)  $\frac { x ^ { 9 } - 4 } { 4 x ^ { 5 } } + \ln x ^ { 2 } - e ^ { - 4 x } + c$ 
D)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + 2 \ln x - e ^ { - 4 x } + c$ 
E)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + 0.5 \ln x + e ^ { - 4 x } + c$ 
A)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + \ln x ^ { 2 } + e ^ { - 4 x } + c$ 
B)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + 2 \ln x ^ { 2 } - e ^ { - 4 x } + c$ 
C)  $\frac { x ^ { 9 } - 4 } { 4 x ^ { 5 } } + \ln x ^ { 2 } - e ^ { - 4 x } + c$ 
D)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + 2 \ln x - e ^ { - 4 x } + c$ 
E)  $\frac { x ^ { 9 } + 4 } { 4 x ^ { 5 } } + 0.5 \ln x + e ^ { - 4 x } + c$ A

Question 4

The producer's surplus at Q = a for the supply function P = 6 + 8Q
Is known to be 400. Find the value of a.

Accepted Answer

A) 25 
B) 5 
C) 20 
D) 10 
E) 15 
A) 25 
B) 5 
C) 20 
D) 10 
E) 15

Question 5

A firm's marginal revenue and marginal cost functions are given by 
MR = 240 - 0.6Q2 and MC = 150 + 0.3Q2
If fixed costs are 50, determine the maximum profit.

Accepted Answer

A) 200 
B) 550 
C) 800 
D) 650 
E) 150 
A) 200 
B) 550 
C) 800 
D) 650 
E) 150

Question 6

If the investment flow is $I ( t ) = 5000 t ^ { \frac { 1 } { 4 } }$ calculate the capital formation from the end of the second year to half- way through the fifth year. Give your answer to the nearest whole number.

Accepted Answer

A) 33,691 
B) 20,879 
C) 16,703 
D) 26,217 
E) 24,177 
A) 33,691 
B) 20,879 
C) 16,703 
D) 26,217 
E) 24,177

Question 7

Which of the following represents the consumption function when
$M P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }$, and $C = 50$ when $Y = 100$ ?

Accepted Answer

A)  $0.4 Y + 0.2 \sqrt { Y } + 8$ 
B)  $0.4 Y + 0.2 \sqrt { Y } + 50$ 
C)  $0.4 Y + 0.05 \sqrt { Y } + 50$ 
D)  $0.4 Y - 0.2 \sqrt { Y } + 50$ 
E)  $0.4 Y - 0.05 \sqrt { Y } + 5$ 
A)  $0.4 Y + 0.2 \sqrt { Y } + 8$ 
B)  $0.4 Y + 0.2 \sqrt { Y } + 50$ 
C)  $0.4 Y + 0.05 \sqrt { Y } + 50$ 
D)  $0.4 Y - 0.2 \sqrt { Y } + 50$ 
E)  $0.4 Y - 0.05 \sqrt { Y } + 5$

Question 8

Which of the following is an expression for g'(x)when
$g ( x ) = \int _ { 2 } ^ { x } \left( 5 t ^ { 2 } - 2 t \right) d t ?$

Accepted Answer

A)  $5 t ^ { 2 } - 2 t$ 
B)  $5 x ^ { 2 } - 2 x$ 
C)  $\frac { 5 } { 3 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 }$ 
D)  0 
E)  $\frac { 5 } { 3 } t ^ { 3 } - \frac { 2 } { 3 } t ^ { 2 }$ 
A)  $5 t ^ { 2 } - 2 t$ 
B)  $5 x ^ { 2 } - 2 x$ 
C)  $\frac { 5 } { 3 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 }$ 
D)  0 
E)  $\frac { 5 } { 3 } t ^ { 3 } - \frac { 2 } { 3 } t ^ { 2 }$

Question 9

Evaluate $\int _ { - 1 } ^ { 2 } 5 x ^ { 2 } - 4 x + 6 d x$

Accepted Answer

A)  $11 \frac { 2 } { 3 }$ 
B)  27 
C)  $23 \frac { 2 } { 3 }$ 
D)  $15 \frac { 2 } { 3 }$ 
E)  21 
A)  $11 \frac { 2 } { 3 }$ 
B)  27 
C)  $23 \frac { 2 } { 3 }$ 
D)  $15 \frac { 2 } { 3 }$ 
E)  21

Question 10

Find the consumer's surplus at Q = 8 for the demand function P = 50 - 4Q.

Accepted Answer

A) 272 
B) 256 
C) 298 
D) 192 
E) 128 
A) 272 
B) 256 
C) 298 
D) 192 
E) 128

Evaluate $\int _ { 2 } ^ { 10 } \frac { 1 } { ( 2 x + 5 ) \sqrt { ( 2 x + 5 ) } } d x$

Which of the following expressions represents the present value of a continuous revenue stream for n years at a constant rate of $S per year if the discount rate is r%?

Find $\int x ^ { 3 } - \frac { 5 } { x ^ { 6 } } + \frac { 2 } { x } - 4 e ^ { - 4 x } d x$

The producer's surplus at Q = a for the supply function P = 6 + 8Q Is known to be 400. Find the value of a.

A firm's marginal revenue and marginal cost functions are given by MR = 240 - 0.6Q2 and MC = 150 + 0.3Q2 If fixed costs are 50, determine the maximum profit.

If the investment flow is $I ( t ) = 5000 t ^ { \frac { 1 } { 4 } }$ calculate the capital formation from the end of the second year to half- way through the fifth year. Give your answer to the nearest whole number.

Which of the following represents the consumption function when $M P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }$ , and $C = 50$ when $Y = 100$ ?

Which of the following is an expression for g'(x)when $g ( x ) = \int _ { 2 } ^ { x } \left( 5 t ^ { 2 } - 2 t \right) d t ?$

Evaluate $\int _ { - 1 } ^ { 2 } 5 x ^ { 2 } - 4 x + 6 d x$

Find the consumer's surplus at Q = 8 for the demand function P = 50 - 4Q.

Linear Equations

Non-Linear Equations

Mathematics of Finance

Differentiation

Partial Differentiation

Matrices

Linear Prgamming

Dynamics

Filters

Exam 6: Integration

Evaluate ∫2101(2x+5)(2x+5)dx\int _ { 2 } ^ { 10 } \frac { 1 } { ( 2 x + 5 ) \sqrt { ( 2 x + 5 ) } } d x∫210​(2x+5)(2x+5)​1​dx

Which of the following expressions represents the present value of a continuous revenue stream for n years at a constant rate of $S per year if the discount rate is r%?

Find ∫x3−5x6+2x−4e−4xdx\int x ^ { 3 } - \frac { 5 } { x ^ { 6 } } + \frac { 2 } { x } - 4 e ^ { - 4 x } d x∫x3−x65​+x2​−4e−4xdx

The producer's surplus at Q = a for the supply function P = 6 + 8Q Is known to be 400. Find the value of a.

A firm's marginal revenue and marginal cost functions are given by MR = 240 - 0.6Q2 and MC = 150 + 0.3Q2 If fixed costs are 50, determine the maximum profit.

If the investment flow is I(t)=5000t14I ( t ) = 5000 t ^ { \frac { 1 } { 4 } }I(t)=5000t41​ calculate the capital formation from the end of the second year to half- way through the fifth year. Give your answer to the nearest whole number.

Which of the following represents the consumption function when MPC=0.4+0.1YM P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }MPC=0.4+Y​0.1​ , and C=50C = 50C=50 when Y=100Y = 100Y=100 ?

Which of the following is an expression for g'(x)when g(x)=∫2x(5t2−2t)dt?g ( x ) = \int _ { 2 } ^ { x } \left( 5 t ^ { 2 } - 2 t \right) d t ?g(x)=∫2x​(5t2−2t)dt?

Evaluate ∫−125x2−4x+6dx\int _ { - 1 } ^ { 2 } 5 x ^ { 2 } - 4 x + 6 d x∫−12​5x2−4x+6dx

Find the consumer's surplus at Q = 8 for the demand function P = 50 - 4Q.

Linear Equations

Non-Linear Equations

Mathematics of Finance

Differentiation

Partial Differentiation

Matrices

Linear Prgamming

Dynamics

Filters

Evaluate $\int _ { 2 } ^ { 10 } \frac { 1 } { ( 2 x + 5 ) \sqrt { ( 2 x + 5 ) } } d x$

Find $\int x ^ { 3 } - \frac { 5 } { x ^ { 6 } } + \frac { 2 } { x } - 4 e ^ { - 4 x } d x$

If the investment flow is $I ( t ) = 5000 t ^ { \frac { 1 } { 4 } }$ calculate the capital formation from the end of the second year to half- way through the fifth year. Give your answer to the nearest whole number.

Which of the following represents the consumption function when $M P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }$ , and $C = 50$ when $Y = 100$ ?

Which of the following is an expression for g'(x)when $g ( x ) = \int _ { 2 } ^ { x } \left( 5 t ^ { 2 } - 2 t \right) d t ?$

Evaluate $\int _ { - 1 } ^ { 2 } 5 x ^ { 2 } - 4 x + 6 d x$