Evaluate Using L'Hospital's Rule

Problem

(lim_x→8)(ln(x)/√(,x))

Solution

1. Identify the limit type by substituting x=8 into the expression.

2. Evaluate the numerator and denominator at the limit point to see if the expression is indeterminate.

ln(8)=ln(8)

√(,8)=2√(,2)

3. Determine if L'Hospital's Rule is applicable. Since the limit evaluates to a finite value ln(8)/(2√(,2)) and not an indeterminate form like 0/0 or ∞/∞ L'Hospital's Rule is not required.

4. Simplify the resulting expression using logarithmic properties if desired.

ln(8)=ln(2)=3*ln(2)

5. Substitute the values back into the limit expression to find the final result.

(3*ln(2))/(2√(,2))

Final Answer

(lim_x→8)(ln(x)/√(,x))=(3*ln(2))/(2√(,2))

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