Question 1

If two resistors with resistances  and  are connected in parallel,as in the figure,then the total resistance  measured in ohms ($ \Omega$),is given by  . If  and  are increasing at rates of  and  respectively,how fast is  changing when  and  ?
Round the result to the nearest thousandth. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

C

Question 2

Find the tangent line to the ellipse  at the point  .
A) 
B) 
C) 
D) 
E) None of these

Accepted Answer

D

Question 3

Gravel is being dumped from a conveyor belt at a rate of 32 ft/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is 10 ft high? Round the result to the nearest hundredth. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

D

Question 4

A plane flying horizontally at an altitude of 1 mi and a speed of 520 mi/h passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A plane flying horizontally at an altitude...

Question 5

Find dy/dx by implicit differentiation.

Accepted Answer

The answer of Find dy/dx by implicit differentiation. ...

Question 6

Use the linear approximation of the function  at  to approximate the number  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the linear approximation of the function...

Question 7

If a snowball melts so that its surface area decreases at a rate of  ,find the rate at which the diameter decreases when the diameter is 35 cm.

Accepted Answer

The answer of If a snowball melts so that its...

Question 8

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.0018 cm thick to a hemispherical dome with diameter 50 m.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use differentials to estimate the amount of...

Question 9

Find an equation of the tangent line to the given curve at the indicated point.

Accepted Answer

The answer of Find an equation of the tangent line...

Question 10

The curve with the equation  is called an asteroid.Find an equation of the tangent to the curve at the point (  ,1).

Accepted Answer

The answer of The curve with the equation  is...

Question 11

The circumference of a sphere was measured to be 88 cm with a possible error of 0.7 cm.Use differentials to estimate the maximum error in the calculated volume.

Accepted Answer

The answer of The circumference of a sphere was measured...

Question 12

Two cars start moving from the same point.One travels south at 50 mi/h and the other travels west at 40 mi/h.At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Two cars start moving from the same...

Question 13

Calculate  . 
A) 
B) 
C) 
D) 
E) none of these

Accepted Answer

The answer of Calculate  . 
A) 
B) 
C) 
D)...

Question 14

Find the differential of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the differential of the function. 
A)...

Question 15

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat.If the rope is pulled in at a rate of 1 m/s how fast is the boat approaching the dock when it is 7 m from the dock? Round the result to the nearest hundredth if necessary.

Accepted Answer

The answer of A boat is pulled into a dock...

Question 16

Determine the values of x for which the given linear approximation is accurate to within 0.07 at a = 0. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Determine the values of x for which...

Question 17

The top of a ladder slides down a vertical wall at a rate of 0.1 m/s .At the moment when the bottom of the ladder is 3 m from the wall,it slides away from the wall at a rate of 0.2 m/s .How long is the ladder?
A) 2 m
B) 2.8 m
C) 2.3 m
D) 7 m
E) None of these

Accepted Answer

Using the Pythagorean theorem and related rates, the length of the ladder is calculated as 7 m.

Question 18

Two carts,A and B,are connected by a rope 39 ft long that passes over a pulley (see the figure below).The point Q is on the floor 12 ft directly beneath and between the carts.Cart A is being pulled away from Q at a speed of 2 ft/s.How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q?

Accepted Answer

The answer of Two carts,A and B,are connected by a...

Question 19

A baseball diamond is a square with side 90 ft.A batter hits the ball and runs toward first base with a speed of 32 ft/s.At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Accepted Answer

The answer of A baseball diamond is a square with...

Question 20

Two sides of a triangle are 2 m and 3 m in length and the angle between them is increasing at a rate of 0.07 rad/s.Find the rate at which the area of the triangle is increasing when the Angle between the sides of fixed length is  
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Two sides of a triangle are 2...

Quiz 2: Derivatives

If two resistors with resistances and are connected in parallel,as in the figure,then the total resistance measured in ohms ( Ω \OmegaΩ ) ,is given by . If and are increasing at rates of and respectively,how fast is changing when and ? Round the result to the nearest thousandth.

Find the tangent line to the ellipse at the point .

A plane flying horizontally at an altitude of 1 mi and a speed of 520 mi/h passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

Find dy/dx by implicit differentiation.

Use the linear approximation of the function at to approximate the number .

If a snowball melts so that its surface area decreases at a rate of ,find the rate at which the diameter decreases when the diameter is 35 cm.

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.0018 cm thick to a hemispherical dome with diameter 50 m.

Find an equation of the tangent line to the given curve at the indicated point.

The curve with the equation is called an asteroid.Find an equation of the tangent to the curve at the point ( ,1).

The circumference of a sphere was measured to be 88 cm with a possible error of 0.7 cm.Use differentials to estimate the maximum error in the calculated volume.

Two cars start moving from the same point.One travels south at 50 mi/h and the other travels west at 40 mi/h.At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.

Calculate .

Find the differential of the function.

Determine the values of x for which the given linear approximation is accurate to within 0.07 at a = 0.

The top of a ladder slides down a vertical wall at a rate of 0.1 m/s .At the moment when the bottom of the ladder is 3 m from the wall,it slides away from the wall at a rate of 0.2 m/s .How long is the ladder?

A baseball diamond is a square with side 90 ft.A batter hits the ball and runs toward first base with a speed of 32 ft/s.At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Two sides of a triangle are 2 m and 3 m in length and the angle between them is increasing at a rate of 0.07 rad/s.Find the rate at which the area of the triangle is increasing when the Angle between the sides of fixed length is