Homework

Problem 1

Evaluate lim x->3 of x + 5

Problem 2

Evaluate lim x->4 of 2x - 1

Problem 3

Evaluate lim x->-2 of x^2 + 3x

Problem 4

Evaluate lim x->2 of (x^2 - 4)/(x - 2)

Problem 5

Evaluate lim x->3 of (x^2 - 9)/(x - 3)

Problem 6

Evaluate lim x->5 of (x^2 - 25)/(x - 5)

Problem 7

Evaluate lim x->1 of (x^2 - 1)/(x - 1)

Problem 8

Evaluate lim x->-2 of (x^2 - 4)/(x + 2)

Problem 9

Evaluate lim x->0 of sin(x)/x

Problem 10

Simplify x + x

Problem 11

Simplify 3x + 2x

Problem 12

Expand (x + 1)^2

Problem 13

Expand (x + 2)^2

Problem 14

Evaluate lim x->2 of x^2 + 3x

Problem 15

Evaluate lim x->-1 of 4x^2 - x

Problem 16

Evaluate lim x->2 of (x^2 + x - 6)/(x - 2)

Problem 17

Evaluate lim x->3 of (x^2 - 5x + 6)/(x - 3)

Problem 18

Evaluate lim x->1 of (x^2 + x - 2)/(x - 1)

Problem 19

Evaluate lim x->4 of (sqrt(x) - 2)/(x - 4)

Problem 20

Evaluate lim x->0 of (sqrt(x + 9) - 3)/x

Problem 21

If f(x)=x^2, evaluate lim x->3 f(x)

Problem 22

If f(x)=2x+7, evaluate lim x->-2 f(x)

Problem 23

For continuity at x=a, how many conditions must be true?

Problem 24

If the left-hand limit is 4 and the right-hand limit is 4, what is the two-sided limit?

Problem 25

If the left-hand limit is 2 and the right-hand limit is 5, does the two-sided limit exist? Answer yes or no.