Question 1

A kite is 150 feet high and is moving horizontally away from a boy at the rate of 25 feet per second. How fast is the string being paid out when the kite is 390 feet from him?

Accepted Answer

³⁰⁰ / ₁₃ ^{ft / sec.}

Question 2

If  , find  .

Accepted Answer

The answer of If  , find  ....

Question 3

A shark, looking for dinner, is swimming parallel to a straight beach and 80 feet offshore. The shark is swimming at the constant speed of 17 feet per second. At time t = 0, the shark is directly opposite a lifeguard station. How fast is the shark moving away from the lifeguard station when the distance between them is 170 feet?

Accepted Answer

15 ft / sec.

Question 4

Use implicit differentiation to find  if xy = ln(x tan y).

Accepted Answer

The answer of Use implicit differentiation to find  if...

Question 5

A metal cone contracts as it cools. Assume the height of the cone is 20cm and the radius at the base of the cone is 5cm. If the height of the cone is decreasing at 4.0 *10^-⁵cm per second, at what rate is the volume of the cone decreasing when its height is 18.8cm? (Assume the radius is held constant.)

Accepted Answer

The answer of A metal cone contracts as it cools....

Question 6

Find dy/dx by differentiating implicitly. xy = y⁵

Accepted Answer

The answer of Find dy/dx by differentiating implicitly. xy =...

Question 7

Answer true or false. If y + ln(xy) = 9,  .

Accepted Answer

A) True 
 B)False

Question 8

Evaluate.  .

Accepted Answer

The answer of Evaluate.  ....

Question 9

Find the formula for dy if y = cot x.

Accepted Answer

The answer of Find the formula for dy if y...

Question 10

If x2 + y2 = 33, find dy/dx.

Accepted Answer

A)   2 + y2 = 33, find dy/dx. 
A)     
B)     
C)     
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >
B)   2 + y2 = 33, find dy/dx. 
A)     
B)     
C)     
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >
C)   2 + y2 = 33, find dy/dx. 
A)     
B)     
C)     
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >
D)   2 + y2 = 33, find dy/dx. 
A)     
B)     
C)     
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >
E)   2 + y2 = 33, find dy/dx. 
A)     
B)     
C)     
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >

Question 11

The magnetic force F acting on a particle is given by  , where r is the distance from the magnetic source and k is a constant. r is measured to be 2cm with a possible error of ±8%. Estimate the percentage error in F and r.

Accepted Answer

The answer of The magnetic force F acting on a...

Question 12

Answer true or false. If y =  $\pi$cos x - sin x ,  .

Accepted Answer

A) True 
 B)False

Question 13

Find  if  .

Accepted Answer

The answer of Find  if  ....

Question 14

Gravitational force is inversely proportional to the distance between two objects squared. If F =  at a distance d = 2m, how fast is the force diminishing if the objects are moving away from each other at 0.1 m/s?

Accepted Answer

A)   1 N/s
B)   -1 N/s
C)   -10 N/s
D)   10 N/s
E)   0 N/s

Question 15

Evaluate.

Accepted Answer

The answer of Evaluate. ...

Question 16

The power in watts for a circuit is given by P = I 2R. How fast is the power changing if the resistance, R, of the circuit is 1,400  $\Omega$, the current, I, is 1.5A, and the current is decreasing with respect to time at a rate of 0.025 A/s. (Assume R is a constant.)

Accepted Answer

A)   105 w/s
B)   4,200 w/s
C)   26.25 w/s
D)   157.5 w/s
E)   -105 w/s

Question 17

Answer true or false. A circular spill is spreading so that when its radius r is 1 m, dr = 0.005 m. The corresponding change in the area covered by the spill, A, is, to the nearest hundredth of a square meter, 0.008 m2.

Accepted Answer

A) True 
 B)False

Question 18

Evaluate.

Accepted Answer

The answer of Evaluate. ...

Question 19

Find the formula for $\Delta$y if y = 3x⁴ - 9.

Accepted Answer

The answer of Find the formula for $\Delta$y if y...

Question 20

A spherical balloon is inflated so that its volume is increasing at the rate of 30 cubic feet per minute. How fast is the surface area of the balloon increasing when the radius is 5 feet? [Use and S = 4 $\pi$0r².]

Accepted Answer

The answer of A spherical balloon is inflated so that...

Exam 3: Topics in Deifferentiation

A kite is 150 feet high and is moving horizontally away from a boy at the rate of 25 feet per second. How fast is the string being paid out when the kite is 390 feet from him?

If , find .

Use implicit differentiation to find if xy = ln(x tan y).

Find dy/dx by differentiating implicitly. xy = y⁵

Answer true or false. If y + ln(xy) = 9, .

Evaluate. .

Find the formula for dy if y = cot x.

If x² + y² = 33, find dy/dx.

The magnetic force F acting on a particle is given by , where r is the distance from the magnetic source and k is a constant. r is measured to be 2cm with a possible error of ±8%. Estimate the percentage error in F and r.

Answer true or false. If y = $\pi$ ^cos^{x -}^sin^x , $Answer true or false. If y = \pi <sup>cos</sup><sup> x - </sup><sup>sin</sup><sup> x</sup> , .$ .

Find if .

Gravitational force is inversely proportional to the distance between two objects squared. If F = at a distance d = 2m, how fast is the force diminishing if the objects are moving away from each other at 0.1 m/s?

Evaluate.

The power in watts for a circuit is given by P = I ²R. How fast is the power changing if the resistance, R, of the circuit is 1,400 $\Omega$ , the current, I, is 1.5A, and the current is decreasing with respect to time at a rate of 0.025 A/s. (Assume R is a constant.)

Answer true or false. A circular spill is spreading so that when its radius r is 1 m, dr = 0.005 m. The corresponding change in the area covered by the spill, A, is, to the nearest hundredth of a square meter, 0.008 m².

Evaluate.

Find the formula for $\Delta$ y if y = 3x⁴ - 9.

Exam 3: Topics in Deifferentiation

A kite is 150 feet high and is moving horizontally away from a boy at the rate of 25 feet per second. How fast is the string being paid out when the kite is 390 feet from him?

If , find .

Use implicit differentiation to find if xy = ln(x tan y).

Find dy/dx by differentiating implicitly. xy = y5

Answer true or false. If y + ln(xy) = 9, .

Evaluate. .

Find the formula for dy if y = cot x.

If x2 + y2 = 33, find dy/dx.

The magnetic force F acting on a particle is given by , where r is the distance from the magnetic source and k is a constant. r is measured to be 2cm with a possible error of ±8%. Estimate the percentage error in F and r.

Answer true or false. If y = π\piπ cos x - sin x , .

Find if .

Gravitational force is inversely proportional to the distance between two objects squared. If F = at a distance d = 2m, how fast is the force diminishing if the objects are moving away from each other at 0.1 m/s?

Evaluate.

The power in watts for a circuit is given by P = I 2R. How fast is the power changing if the resistance, R, of the circuit is 1,400 Ω\OmegaΩ , the current, I, is 1.5A, and the current is decreasing with respect to time at a rate of 0.025 A/s. (Assume R is a constant.)

Answer true or false. A circular spill is spreading so that when its radius r is 1 m, dr = 0.005 m. The corresponding change in the area covered by the spill, A, is, to the nearest hundredth of a square meter, 0.008 m2.

Evaluate.

Find the formula for Δ\DeltaΔ y if y = 3x4 - 9.

A spherical balloon is inflated so that its volume is increasing at the rate of 30 cubic feet per minute. How fast is the surface area of the balloon increasing when the radius is 5 feet? [Use and S = 4 π\piπ 0r2.]

Find dy/dx by differentiating implicitly. xy = y⁵

If x² + y² = 33, find dy/dx.

Answer true or false. If y = $\pi$ ^cos^{x -}^sin^x , $Answer true or false. If y = \pi <sup>cos</sup><sup> x - </sup><sup>sin</sup><sup> x</sup> , .$ .

The power in watts for a circuit is given by P = I ²R. How fast is the power changing if the resistance, R, of the circuit is 1,400 $\Omega$ , the current, I, is 1.5A, and the current is decreasing with respect to time at a rate of 0.025 A/s. (Assume R is a constant.)

Answer true or false. A circular spill is spreading so that when its radius r is 1 m, dr = 0.005 m. The corresponding change in the area covered by the spill, A, is, to the nearest hundredth of a square meter, 0.008 m².

Find the formula for $\Delta$ y if y = 3x⁴ - 9.