Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Add $1$ and $0$ .

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

Step 3.1.2

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

$\frac{0}{x}$

Step 3.2

Divide $0$ by $x$ .

$0$