# Calculus 2 : Finding Limits and One-Sided Limits

## Example Questions

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### Example Question #1 : Finding Limits And One Sided Limits

Which graph is a possible sketch of the function  that possesses the following characteristics:

There does not exist such a graph.

Explanation:

Since  there is a possible vertical asymptote at .

As we approach from the left, the graph should tend to . Approaching  from the right, the graph tends to .

The only graph that does so is  .

### Example Question #2 : Finding Limits And One Sided Limits

The graph above is a sketch of the function . Find .

Does not exist

Explanation:

We need to look at the behavior of the function as it tends to  from the left.  Therefore the answer is

### Example Question #3 : Finding Limits And One Sided Limits

The graph above is a sketch of . Find .

Does not exist

Does not exist

Explanation:

The limit does not exist because the one-sided limits are not equal; , whereas

### Example Question #4 : Finding Limits And One Sided Limits

Determine the value of .

Explanation:

The expression  indicates that all points on the domain are equal to 5 since the absolute value negates negative values.

The  is to search for the limit as the graph approaches  from the left side of the graph.  Since the absolute value of negative five is five, the graph approaches five from the left.

### Example Question #5 : Finding Limits And One Sided Limits

Evaluate the following limit.

Limit does not exist

Explanation:

This limit can be solved using simple manipulation of the expression inside the limit:

### Example Question #6 : Finding Limits And One Sided Limits

Evaluatle the limit:

Explanation:

Consider the domain of the function. Because this equation is a polynomial, x is not restricted by any value. Thus the way to evaluate this limit would simply be to plug the value that x is approaching into the limit equation.

### Example Question #7 : Finding Limits And One Sided Limits

Evaluate the limit:

Explanation:

Consider the domain of the function. Because this equation is a polynomial, x is not restricted by any value. Thus the way to evaluate this limit would simply be to plug the value that x is approaching into the limit equation.

### Example Question #8 : Finding Limits And One Sided Limits

Evaluate the limit:

Explanation:

The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=-2; so we proceed to insert the value of x into the entire equation.

### Example Question #9 : Finding Limits And One Sided Limits

Evaluate the limit:

Explanation:

The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=0; so we proceed to insert the value of x into the entire equation.

### Example Question #10 : Finding Limits And One Sided Limits

Evaluate the limit: