AP Calculus ABeasymcq1 pt

What is the value of limx0ln(x+1)x2+x\lim_{x \to 0} \frac{\ln(x + 1)}{x^2 + x}?

A.11
B.00
C.Does not exist
D.1-1

Explanation

Core Concept

Correct. Direct substitution yields the indeterminate form 0/00/0. Applying L'Hôpital's Rule by differentiating the numerator and denominator gives 1/(x+1)2x+1\frac{1/(x+1)}{2x+1}, which evaluates to 1/1=11/1 = 1 at x=0x=0.

Correct Answer

A11

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