Chapter 11 Test REVIEW

Name________________________________________________ Date ____________________ Period _____ Row _____ Pre Calculus Chapter 11 Test REVIEW Graph the function. Then use your graph to find the x3 + 12x2 - 5x 5) lim indicated limit. 5x x¬0 1) f(x) = x + 1 if x < 0 , lim f(x) 3x + 1 if x ≥ 0 x¬0 y

6) lim (x - 4)( x - 2) x¬4 x

2) f(x) = 4x ,

A piecewise function is given. Use the function to find the indicated limits, or state that a limit does not exist. lim lim lim (a) f(x), (b) f(x), and (c) f(x) x¬dx¬d+ x¬d 1 if x > 1 7) f(x) = x - 1 ; d=1

lim f(x) x¬-3

x2 + 2x if x ≤ 1

y

5

y

4 3 2

x

1 -5 -4 -3 -2 -1 -1 -2 -3 -4

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied. lim x3 - 4x - 12 3) x¬0 x-2

-5

4) lim x2 - 5 x¬0

1

1

2

3

4

5 x

8) f(x) =

-5x - 1 if x < 1 ; -7x + 1 if x > 1 5

Find the derivative of f at x. That is, find f (x). 13) f(x) = 3x - 9; x = 3

d=1

y

4 3 2 1 -5 -4 -3 -2 -1 -1

1

2

3

4

14) f(x) = x2 - 8x - 17; x = 4

5 x

-2 -3 -4 -5

Solve the problem.

Determine whether f is continuous at a. 3 9) f(x) = x+4

15) The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 2 inches to 2.1 inches.

a = -4

10) f(x) =

8 x+5

a=0 16) The function f(x) = 4px2 describes the volume , f(x), of a right circular cylinder of height 4 feet and radius x feet. If the radius is changing, find the instantaneous rate of change of the volume with respect to the radius when the radius is 8 feet. Leave answer in terms of p.

Find the slope of the tangent line to the graph of f at the given point. 11) f(x) = x2 + 5x at (4, 36)

12) f(x) = -4x + 27 at (6, 3)

2