Find the exact value of each of the following limits. Note that finding the exact value requires that the limit be found analytically rather than numerically.
Careful! Be sure to check:
For a limit to exist, the limit from the left must agree with the limit from the right.
We know that
Recognize that this is Hana's Definition of the Derivative, and find
, or use l'Hopital's Rule. , which is also an indeterminate form.
Before using l'Hopital's Rule, you will need to convert the argument into a single fraction that
To solve this limit, you will have to use l'Hopital's Rule twice.
To convert this limit into
form, let , then write the argument as a single fraction.
See hint in part (a).