Question 1

An aircraft is climbing at a 30° angle to the horizontal. Find the aircraft's speed if it is gaining altitude at the rate of 250 miles per hour.

Accepted Answer

The answer of An aircraft is climbing at a 30°...

Question 2

y = x8. Find the formula for dy.

Accepted Answer

A)  dy = 8x7 
B)  dy = 8(x + dx)7 
C)  dy = 8x7 - 8(dx)7 
D)  dy = (x + dx)8 - x8 
E)  dy = 8x7dx

Question 3

Evaluate.  .

Accepted Answer

The answer of Evaluate.  ....

Question 4

Answer true or false. A cube is expanding as temperature increases. If the length of the cube is changing at a rate of dx = 0.6 mm when x is 3.5 m, the volume is experiencing a corresponding change of 22,050,000 mm3.

Accepted Answer

A) True 
 B)False

Question 5

Answer true or false. If A = 8xy, then

Accepted Answer

A) True 
 B)False

Question 6

Answer true or false. If y2 = 8x, dy/dx = 8.

Accepted Answer

A) True 
 B)False

Question 7

The edge of a cube of side x is contracting. At a certain instant, the rate of change of the surface area is equal to 6 times the rate of change of its edge. Find the length of the edge.

Accepted Answer

The answer of The edge of a cube of side...

Question 8

An angler has a fish at the end of his line, which is being reeled in at the rate of 3 feet per second from a bridge 50 feet above the water. At what speed is the fish moving through the water towards the bridge when the amount of line out is 130 feet? (Assume the fish is at the surface of the water and that there is no sag in the line.)

Accepted Answer

The answer of An angler has a fish at the...

Question 9

A 10-ft ladder rests against a wall at  $\pi$/4 radians. If it were to begin to slip, when the bottom of the ladder is moving at 0.08 ft/s, how fast would the top of the ladder be moving down the wall? (How fast would the height of the upper end of the ladder on the side of the wall be changing?)

Accepted Answer

A)  0.074 ft/s 
B)  0.071 ft/s 
C)  0.069 ft/s 
D)  0.080 ft/s 
E)  0.088 ft/s

Question 10

Use dy to approximate  starting at x = 9.

Accepted Answer

A)  3.003 
B)  9.003 
C)  2.997 
D)  3.001 
E)  3.167

Question 11

The pressure P, the volume V, and the temperature T of an enclosed gas are related by the Ideal Gas Law, PV = kT where k is a constant. With the temperature held constant, the volume of the gas is calculated from a measured value of its pressure. Estimate the maximum permissible error in the pressure measurement if the percentage error in the volume must be kept to within ±3%.

Accepted Answer

The answer of The pressure P, the volume V, and...

Exam 3: Topics in Deifferentiation

An aircraft is climbing at a 30° angle to the horizontal. Find the aircraft's speed if it is gaining altitude at the rate of 250 miles per hour.

y = x⁸. Find the formula for dy.

Evaluate. .

Answer true or false. A cube is expanding as temperature increases. If the length of the cube is changing at a rate of dx = 0.6 mm when x is 3.5 m, the volume is experiencing a corresponding change of 22,050,000 mm³.

Answer true or false. If A = 8xy, then

Answer true or false. If y² = 8x, dy/dx = 8.

The edge of a cube of side x is contracting. At a certain instant, the rate of change of the surface area is equal to 6 times the rate of change of its edge. Find the length of the edge.

A 10-ft ladder rests against a wall at $\pi$ /4 radians. If it were to begin to slip, when the bottom of the ladder is moving at 0.08 ft/s, how fast would the top of the ladder be moving down the wall? (How fast would the height of the upper end of the ladder on the side of the wall be changing?)

Use dy to approximate starting at x = 9.

Exam 3: Topics in Deifferentiation

An aircraft is climbing at a 30° angle to the horizontal. Find the aircraft's speed if it is gaining altitude at the rate of 250 miles per hour.

y = x8. Find the formula for dy.

Evaluate. .

Answer true or false. A cube is expanding as temperature increases. If the length of the cube is changing at a rate of dx = 0.6 mm when x is 3.5 m, the volume is experiencing a corresponding change of 22,050,000 mm3.

Answer true or false. If A = 8xy, then

Answer true or false. If y2 = 8x, dy/dx = 8.

The edge of a cube of side x is contracting. At a certain instant, the rate of change of the surface area is equal to 6 times the rate of change of its edge. Find the length of the edge.

A 10-ft ladder rests against a wall at π\piπ /4 radians. If it were to begin to slip, when the bottom of the ladder is moving at 0.08 ft/s, how fast would the top of the ladder be moving down the wall? (How fast would the height of the upper end of the ladder on the side of the wall be changing?)

Use dy to approximate starting at x = 9.

y = x⁸. Find the formula for dy.

Answer true or false. A cube is expanding as temperature increases. If the length of the cube is changing at a rate of dx = 0.6 mm when x is 3.5 m, the volume is experiencing a corresponding change of 22,050,000 mm³.

Answer true or false. If y² = 8x, dy/dx = 8.

A 10-ft ladder rests against a wall at $\pi$ /4 radians. If it were to begin to slip, when the bottom of the ladder is moving at 0.08 ft/s, how fast would the top of the ladder be moving down the wall? (How fast would the height of the upper end of the ladder on the side of the wall be changing?)