Finding Limits Graphically & Numerically
Finding Limits Analytically
Continuity & One-Sided Limits
Infinite Limits & Vertical Asymptotes
Drawing Graphs

100

Estimate the limit by completing the following chart:

approx 0.25

100

Find: 

lim_(x->0) (5x-3)

-3

100

Find: 

lim_(x->5^-) f(x)

-3

100

Find: 

lim_(x->(pi/2)^+) tan x

-oo

100

Draw and label a graph of f(x) where:

lim_(x->1) f(x) = DNE

*Answers will vary*

200

Find: 

lim_(x->-5) f(x)

lim_(x->-5) f(x) = 2

200

Find: 

lim_(x->4) (5)/(x-1)

5/3

200

Find: 

lim_(x->6^+) (x-6)/(x^2-36)

1/12

200

Find: 

lim_(x->4^-) (-1)/(x-4)

oo

200

Draw and label a graph of f(x) where:

lim_(x->-2^+) f(x) = oo

lim_(x->-2^-) f(x) = -oo

*Answers will vary*

300

Find: 

lim_(x->-2) f(x)

lim_(x->-2) f(x) = DNE

300

Find: 

lim_(x->pi) (1-sinx)/(cos x)

-1

300

Find: 

lim_(x->4^-) (abs(x-4))/(x-4)

-1

300

Find: 

lim_(x->4^+) (-1)/(x-4)

-oo

300

Draw and label a graph of f(x) where:

lim_(x->-2^-) f(x) = -0.5

lim_(x->-2^+) f(x) = 2

lim_(x->3) f(x) = DNE



*Answers will vary*

400

Find: 

lim_(x->0) f(x)

lim_(x->0) f(x) = 6

400

Find: 

lim_(x->0) (sqrt(4+x) - 2)/(x)

1/4

400

1. Find all x-values where f(x) is discontinuous. 

2. State which x-values are removable and non-removable.

3. Write the intervals on which f(x) is continuous.

f(x) = (x^2-7x)/(3x^3-19x^2-14x)

1. x = -2/3, 0, 7

2. removable at x=0, x=7; non-removable at x=-2/3

3. x in (-oo, -2/3)U(-2/3,0)U(0,7)U(7,oo)



400

Find: 

lim_(x->0^-) 1+1/x

-oo

400

Draw and label a graph of f(x) where:

f(2)=8; f(7)=-8

lim_(x->2^+)f(x)=6; lim_(x->2)f(x)=DNE; lim_(x->7)f(x)=-6





*Answers will vary*

500

Find: 

lim_(x->4) f(x)

lim_(x->4) f(x) = DNE

500

Find: 

lim_(x->0) (1/sqrt(1+x)-1)/x

-1/2

500

Find:

12

500

Find: 

lim_(x->0^+) x+1/x+3

oo

500

Draw and label a graph of f(x) where:

f(-5)=1; f(-2)=2;f(1)=7;f(3)=undef.;

f(4)=f(5)=1;

lim_(x->-5)f(x)=2; lim_(x->-2)f(x)=DNE; lim_(x->4^+)f(x)=-4;

lim_(x->5^-)f(x)=-3


*Answers will vary*