Calculus 2 : Finding Limits and One-Sided Limits
Study concepts, example questions & explanations for Calculus 2
All Calculus 2 Resources
Example Questions
Example Question #81 :Limits
Given the graph of the function
Examining the graph, we want to find where the graph tends to as it approaches zero from the left hand side. We can see that there appears to be a vertical asymptote at zero. As the x values approach zero from the left the function values of the graph tend towards positive infinity.
Therefore, we can observe that
Example Question #82 :Limits
Given the graph of the function
Examining the graph, we want to find where the graph tends to as it approaches zero from the right hand side. We can see that there appears to be a vertical asymptote at zero. As the x values approach zero from the right the function values of the graph tend towards positive infinity.
Therefore, we can observe that
Example Question #83 :Limits
Evaluate the following limit:
The limit does not exist
To evaluate the limit, simply substitute what we are approaching (5) into the function:
That we are approaching 5 from the left has no impact on the final answer.
Example Question #84 :Limits
Given the graph of
检查上面的图,我们需要看看3个e things:
1) What is the limit of the function as
2) What is the limit of the function as
3) What is the function value as
Therefore, we can observe that
Example Question #1 :Estimating Limits From Graphs And Tables
Given the above graph of
Examining the graph, we want to find where the graph tends to as it approaches zero from the right hand side. We can see that there appears to be a vertical asymptote at zero. As the x values approach zero from the right the function values of the graph tend towards positive infinity.
Therefore, we can observe that
Example Question #85 :Limits
Given the above graph of
Examining the graph, we want to find where the graph tends to as it approaches zero from the left hand side. We can see that there appears to be a vertical asymptote at zero. As the x values approach zero from the left the function values of the graph tend towards negative infinity.
Thus, we can observe that
Example Question #86 :Limits
Evaluate the following limit:
The limit does not exist.
Because this is a one sided limit, we can't simply subsitute the value into the function being evaluated. The function is piecewise, changing from one function
Thus,
Example Question #41 :Finding Limits And One Sided Limits
Given the above graph of
检查上面的图,我们需要看看3个e things:
1) What is the limit of the function as
2) What is the limit of the function as
3) What is the function value as
Thus, we can observe that
Example Question #42 :Finding Limits And One Sided Limits
Given the above graph of
Examining the graph, we want to find where the graph tends to as it approaches zero from the right hand side. We can see that there appears to be a vertical asymptote at zero. As the x values approach zero from the right the function values of the graph tend towards negative infinity.
Therefore,the graph, we can observe that
Example Question #43 :Finding Limits And One Sided Limits
Given the above graph of
Examining the graph, we want to find where the graph tends to as it approaches zero from the left hand side. We can see that there appears to be a vertical asymptote at zero. As the x values approach zero from the left the function values of the graph tend towards positive infinity.
Therefore,the graph, we can observe that
Certified Tutor
Certified Tutor
All Calculus 2 Resources
