Deck 2: Extension G: Limits and Derivatives

Question 1

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

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B)
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D)
E)

Answer 1

Question 2

A plane flying horizontally at an altitude of 1 mi and a speed of 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.

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E)

Answer 2

Question 3

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.

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E)

Answer 3

Question 4

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.

Question 5

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?

Question 6

Gravel is being dumped from a conveyor belt at a rate of 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 ft high? Round the result to the nearest hundredth.

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B)
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E)

Question 7

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

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E)

Question 8

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.

Question 9

The top of a ladder slides down a vertical wall at a rate of 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?

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B)
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D)
E) None of these

Question 10

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.