Calculus Examples

$\frac{lim_{x \to 0} \ln (x + 1)}{\sqrt{x}}$

Evaluate the limit.

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Move the limit inside the logarithm.

$\frac{\ln (lim_{x \to 0} x + 1)}{\sqrt{x}}$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{\ln (lim_{x \to 0} x + lim_{x \to 0} 1)}{\sqrt{x}}$

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$\frac{\ln (lim_{x \to 0} x + 1)}{\sqrt{x}}$

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{\ln (0 + 1)}{\sqrt{x}}$

Simplify the answer.

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Simplify the numerator.

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Add $0$ and $1$ .

$\frac{\ln (1)}{\sqrt{x}}$

The natural logarithm of $1$ is $0$ .

$\frac{0}{\sqrt{x}}$

Divide $0$ by $\sqrt{x}$ .

$0$