limits for test review

Question

 

Answer 1

6)

a)

Apply the limits.

Answer 2

(b)

Therefore .

Answer 3

(c)

Therefore .

Answer 4

(d)

The denominator of the function is zero at x = ±2.

For the limit x > 2, the denominator is not zero and the numerator is a positive value.

Then .

Therefore .

 

Answer 5

(e)

The denominator of the function is zero at x = ±2.

Consider the intervals -2 < x < 2 and x > 2.

For the limit  -2 < x < 2, the denominator is a negative value and the numerator is a positive value.

Then .

For the limit x > 2, the denominator is not zero and the numerator is a positive value.

Then .

Then .

Therefore .

Comments

so is there 2 answers, it can be positive and negative infinity?

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Yes,

For Better understanding, look at the graph.

You can see that in the interval -2<x<2 , the function tends to -∞ and x>2 then function tends ∞.

So It is possible to have two answers.

Answer 6

(a)

Therefore the limit .

Answer 7

(b)

Therefore the limit .

Answer 8

(c)

= (7 - 4)

= 3

Therefore.

Answer 9

(d)

Therefore .

Answer 10

(e)

Therefore .