QuestionFind the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. Need Help? Read It Watch It
Studdy Solution
STEP 1
1. We need to find the limit .
2. The limit is in an indeterminate form as .
3. We can use L'Hospital's Rule to resolve the indeterminate form.
4. Alternatively, we can consider using series expansion for a more elementary method.
STEP 2
1. Verify the indeterminate form.
2. Apply L'Hospital's Rule.
3. Simplify the expression.
4. Evaluate the limit.
STEP 3
Verify the indeterminate form by substituting :
The expression is indeed in the form .
STEP 4
Apply L'Hospital's Rule, which states that for indeterminate forms or , the limit of as can be found by evaluating .
Differentiate the numerator and the denominator:
STEP 5
Substitute the derivatives back into the limit:
STEP 6
Evaluate the limit by substituting :
The value of the limit is:
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