QuestionEvaluate
Studdy Solution
STEP 1
1. We are given the limit expression .
2. We need to evaluate this limit as approaches 7.
STEP 2
1. Substitute into the expression to check for indeterminate form.
2. Simplify the expression using algebraic techniques.
3. Re-evaluate the limit after simplification.
STEP 3
Substitute into the expression:
The expression is in the indeterminate form .
STEP 4
Simplify the expression by rationalizing the numerator. Multiply the numerator and the denominator by the conjugate of the numerator:
STEP 5
Simplify the numerator using the difference of squares:
STEP 6
Factor the denominator:
STEP 7
Substitute the simplified numerator and denominator back into the expression:
Cancel the common factor :
STEP 8
Re-evaluate the limit as approaches 7:
Simplify:
The value of the limit is:
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