# What is thelimitas x approaches negativeinfinityof ?  Hunter

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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