All AP Calculus BC Resources
Example Questions
Example Question #231 :Ap Calculus Bc
Evaluate the following limit:
The limit does not exist
The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.
This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get
Example Question #1 :Estimating Limits From Graphs And Tables
For the piecewise function:
, find.
Any real number.
Does not exist.
The limitindicates that we are trying to find the value of the limit asapproaches to zero from the right side of the graph.
From right to left approaching, the limit approaches to 1 even though the value atof the piecewise function does not exist.
The answer is.
Example Question #2 :Limits
Given the graph ofabove, what is?
Examining the graph of the function above, we need to look at three things:
1) What is the limit of the function as it approaches zero from the left?
2) What is the limit of the function as it approaches zero from the right?
3) What is the function value at zero and is it equal to the first two statements?
If we look at the graph we see that asapproaches zero from the left thevalues approach zero as well. This is also true if we look the values asapproaches zero from the right. Lastly we look at the function value at zero which in this case is also zero.
Therefore, we can observe thatasapproaches.
Example Question #4 :Limits
Given the graph ofabove, what is?
Does not exist
Does not exist
检查上面的图,我们需要看看3个e things:
1) What is the limit of the function asapproaches zero from the left?
2) What is the limit of the function asapproaches zero from the right?
3) What is the function value asand is it the same as the result from statement one and two?
Therefore, we can determine thatdoes not exist, sinceapproaches two different limits from either side :from the left andfrom the right.
Example Question #5 :Limits
Given the above graph of, what is?
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 thatasapproachesfrom the right.
Example Question #41 :Functions, Graphs, And Limits
Given the above graph of, what is?
Does Not Exist
Does Not Exist
Examining the graph, we can observe thatdoes not exist, asis not continuous at. We can see this by checking the three conditions for which a functionis continuous at a point:
A valueexists in the domain of
The limit ofexists asapproaches
The limit ofatis equal to
Given, we can see that condition #1 is not satisfied because the graph has a vertical asymptote instead of only one value forand is therefore an infinite discontinuity at.
We can also see that condition #2 is not satisfied becauseapproaches two different limits:from the left andfrom the right.
Based on the above, condition #3 is also not satisfied becauseis not equal to the multiple values of.
Thus,does not exist.
Example Question #1 :Estimating Limits From Graphs And Tables
Example Question #42 :Functions, Graphs, And Limits
Example Question #1 :Limits
Example Question #1 :Limits
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