# What is thelimitas x approaches negativeinfinityof  ?

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Solution:

Concept:The value   is the value of the function such that the variable x approaches a. This is known as the limiting value of the function at  . For limit to exist, the value of function when x approaches a from left is equal to the value of function when x approaches a from right, which is,

The value of the function at   may vary from its limiting value at  .

Few of the properties of limits are listed as shown below:

1.

2.

3.

4.

5.

There are also some important limits listed as below:

1.

2.

3.

4.

In the cases where any indeterminate form is obtained, the L-Hospital rule is applied which is the differentiation of numerator and denominator separately until the indeterminate form is removed.

Calculation:

Step:1 The function is   and the limit x approaches to   then it is written as,  .

Step:2 Rationalise the expression by multiplying and dividing by  .

Step:3 The value is calculated as shown below by dividing the numerator and denominator by x.

Step:4 Substitute x as  in the expression and simplify as follows:

Thus, the limit value of  is  .

Answer:The limit value of  is  .

Similar Problems:

Problem 1:What is the limit as x approaches infinity of  ?

Solution:

Step:1 The function is   and the limit x approaches to   then it is written as,  .

Step:2 The tangent function has value between   and   for every   interval therefore at infinity, it may have any value in between.

Step:3 Therefore, the value of   for   is not defined.

Thus, the limit   does not exist.

Answer: The limit   does not exist.

Problem 2:What is the limit as x approaches infinity of  ?

Solution:

Step:1 The function is   and the limit x approaches to   then it is written as,  .

Step:2 Since  , use this result and simplify the value of limit as shown below:

Step:3 Replace   by t in the expression and then simplify.

Thus, the limit value of   is 1.

Answer: The limit value of   is 1.

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