Question

45 POINTS Evaluate the limit as h goes to 0 of the quotient of the quantity the 4th power of 3 plus h minus 81 and h. SEE PICTURE ATTACHED.

Answer 1

108

Explanation:

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Whenever you have a limit and the answer to that limit is one of the indeterminant form, you can use the L'Hopital's Rule to solve for the limit.

Indeterminant forms:

`(0)/(0) , (\infty)/(\infty), 0\cdot \infty, \infty - \infty, 0^(0), \infty^(0), 1^(\infty)`

L'Hopitals Rule:

L'Hopitals rule is just taking the derivative of the numerator, and the derivative of the denominator separately.

After doing the L'Hopital's rule, take the limit again. If the result is an actual number then you got your answer.

If the result is another indeterminant form then use L'Hopitals rule again and check the limit again after that. Repeat the process until you get your answer.