Find limits for lim x-->1 ((x^5)-1)/(x-1) Use L'Hospital's Rule when appropriate. If there is a more elementary algebraic method, consider it.
Find limits for lim x-->1 ((x^5)-1)/(x-1)
Use L'Hospital's Rule when appropriate. If there is a more elementary algebraic method, you might consider it.
If you are able to use L' Hopital's Rule and when you convert your expression to a fraction, check and state that the hypotheses of the theorem are satisfied. check problem by graphing the function near the limit and see if the values support your solution.
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To find this limit, we can factor the polynomial in the numerator, and cancel out any common factors.
where in the last two lines the denominator is no longer a problem with the limit and we can use direct substitution.
lim x-->1 ((x^5)-1)/(x-1)
`lim_(x->1) (x^5 - 1)/(x-1)`
If we substitute in 1 for x, we end up with the indeterminate form 0/0. Therefore, we can use L'Hopital's Rule to get:
``which equals 5.
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