All High School Math Resources
Example Questions
Example Question #1 : Calculating Limits
Calculate .
Possible Answers:
The limit does not exist.
Correct answer:
Explanation:
Substitute to rewrite this limit in terms of u instead of x. Multiply the top and bottom of the fraction by 2 in order to make this substitution:
(Note that as ,
.)
, so
, which is therefore the correct answer choice.
Example Question #2 : Calculating Limits
Calculate
Possible Answers:
The limit does not exist.
Correct answer:
Explanation:
You can substitute to write this as:
Note that as ,
, since the fraction becomes indeterminate, we need to take the derivative of both the top and bottom of the fraction.
, which is the correct choice.
Gary
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