Calculus Unit 1 Review

Limits

100

a) -inf

b) inf

c) DNE

d) 5

e) DNE

f) 5

200

Evaluate the limit as x approaches 2 if f(x)= (x^2-2x)/2 .

0

300

Find the limit as x approaches 0 if f(x)= (sqrt(x+3) -sqrt3)/x 

1/2sqrt(3)

400

Find the limit as x approaches 0 if f(x)= ((x-6)^2-36)/x 

-12

Rational Functions

100

Simplify  (x^2+16x+64)/(x^2-2x-80) 

(x+8)/(x-10)

200

Simplify  (21x^3)/(7x^4+35x^3) 

3/(x+5)

300

Find all values that make the expression undefined:

(x^2-81)/(8x+16)

When x = -2

Continuity

100

List the three pieces we need to determine if a function is continuous.

1) f(a) exists

2) lim as x approaches a exists

3) lim as x approaches a = f(a)

200

Given f(x)= {19-4x^2,x>2 and 9-2x, x<2 , is f(x) continuous at 2? Explain.

No, 2 is not included in either function

300

List all values for which the graph is discontinuous on (-9,9). State the type of discontinuity.

x=-5 (removable)

x=-3 (removable)

x=-2 (jump)

x=0 (removable)

x=7 (infinite)

400

Find k that makes the function continuous.

k=-1/2

Derivatives

100

What is the derivative of 3x⁵+4x+7

15x⁴+4

200

What is the derivative of 6ln(x)

6/x

300

What is the derivative of (3x)(5^x)

3(5^x)+3x(5^x)ln5

400

What is the derivative of (7x²)/(3x+4)

(14x(3x+4)-21x²)/(3x+4)²