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helo? find limits

0 votes

asked Aug 11, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(1)

The limit  is .

The above expression is in form as tends to zero.

Thus, find the limit by L-Hospital rule.

L-Hospital rule:

Suppose image or image, then image

Apply L-Hospital rule.

Here and .

.

Differentiate on each side.

.

.

Differentiate on each side.

.

image

.

Solution:

.

answered Aug 11, 2015 by cameron Mentor
edited Aug 11, 2015 by cameron
0 votes

(2)

The limit  is .

Consider .

To estimate the value of limit, construct a table with larger values of  by increasing rapidly.

Observe the table results,

As the value of increases, value is close to zero.

Thus, .

Solution:

.

answered Aug 11, 2015 by cameron Mentor
edited Aug 11, 2015 by cameron
0 votes

(3)

The limit  is .

Apply squeeze theorem:

Suppose that image, where and , then  .

The range of is .

.

Divide on each side by .

image

Apply infinite limits on each side.

image

image.

Therefore, by squeeze theorem image.

Solution:

image.

 

answered Aug 11, 2015 by cameron Mentor
edited Aug 11, 2015 by cameron

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