QuestionFind the limit:
Studdy Solution
STEP 1
Assumptions1. We are finding the limit as x approaches0 from the positive side. . The function we are evaluating is .
STEP 2
The function has an indeterminate form of type0/0 as x approaches0. We can apply L'Hopital's rule, which states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives, provided the original limit is of indeterminate form0/0 or ∞/∞.
where and .
STEP 3
Find the derivative of and .
and .
STEP 4
Substitute and back into the limit.
STEP 5
implify the limit.
STEP 6
Evaluate the limit as x approaches0 from the positive side.
The limit as x approaches0 from the positive side of is .
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