Calculus 2 : Finding Limits and One-Sided Limits
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Example Questions
Example Question #1 : Finding Limits And One Sided Limits
Which graph is a possible sketch of the function 
There does not exist such a graph.
Since 
As we approach 
The only graph that does so is .
Example Question #1 : Finding Limits And One Sided Limits
The graph above is a sketch of the function 
Does not exist
We need to look at the behavior of the function as it tends to 
Example Question #1 : Finding Limits And One Sided Limits
The graph above is a sketch of 
Does not exist
Does not exist
The limit does not exist because the one-sided limits are not equal; 
Example Question #3 : Finding Limits And One Sided Limits
Determine the value of 
The expression 
The 
The correct answer is 
Example Question #2 : Finding Limits And One Sided Limits
Evaluate the following limit.
Limit does not exist
This limit can be solved using simple manipulation of the expression inside the limit:
Example Question #3 : Finding Limits And One Sided Limits
Evaluatle the limit:
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 #4 : Finding Limits And One Sided Limits
Evaluate the limit:
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 #5 : Finding Limits And One Sided Limits
Evaluate the limit:
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 #6 : Finding Limits And One Sided Limits
Evaluate the limit:
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 #7 : Finding Limits And One Sided Limits
Evaluate the limit:
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 equal zero when x=5; so we try to eliminate the denominator by factoring. When the denominator is no longer zero, we may continue to insert the value of x into the remaining equation.
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