FINAL EXAM CALCO #2

324 5xdx

x

30

62 33 5x x dx26

f x

' 1 2sin cos , 0 3f x x x f

Find if

6

2

3

csc

cot

xdxx

7

FIND F’(X)

35 2 5f x x

10

F(X) = (X2 – 4)3/(X + 2), FIND F’(X)

5

F(X) = (SEC5X)4, FIND F’(X)

21

2

dyfind

dx

y x xy

29

sin 1

dyfind

dxx y y

22

A LAMP HANGS 20 FT DIRECTLY ABOVE A STREET ON WHICH A BOY 5 FT TALL IS WALKING. IF THE BOY IS WALKING AWAY FROM THE LIGHT AT THE FATE OF 3 FT/SEC, HOW FAST IS THE BOY’S SHADOW LENGTHENING?

4

A man standing on the top of a 128 foot building and throws a ball straight up in the air at a rate of 96 feet per second.

What is the highest point the ball will reach? What is the speed of the ball the instant that it hits the ground?

24

THE LENGTH OF A RECTANGLE IS DECREASING AT A RATE OF 2 CM/SEC AND THE WIDTH IS INCREASING AT A RATE OF 2 CM/SEC. FIND THE RATE OF CHANGE OF THE AREA WHEN THE LENGTH OF THE RECTANGLE IS 12 CM AND THE WIDTH IS 5 CM.

11

FROM THE EDGE OF A DOCK 12 FEET ABOVE THE SURFACE OF THE WATER, A ROWBOAT IS BEING HAULED IN BY A ROPE AT THE RATE OF 4 FT/SEC. HOW FAST IS THE LENGTH OF THE ROPE CHANGING WHEN THE BOAT IS 5 FEET FROM THE DOCK?

9

A SPHERICAL BALLOON IS LOSING HELIUM AT THE RATE OF 12ΠM3/MIN. FIND THE RATE AT WHICH THE SURFACE AREA IS CHANGING AT THE INSTANT THE BALLOON HAS A RADIUS OF 20M.

16

FIND THE INTERVALS ON WHICH THE FUNCTION IS INCREASING.

3 2( ) 4 6f x x x

20

A CURVE WHOSE SLOPE IS

PASSES THROUGH THE POINT (3, 1). FIND THE COORDINATES OF THE ONLY POINT OF INFLECTION FOR THE GRAPH OF THE CURVE.

2 4x x

13

F(X) = SECX, FIND F’’(X)

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