Calculus Examples

$lim_{x \to 0} \frac{x}{e^{x}}$

Step 1

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

$\frac{lim_{x \to 0} x}{lim_{x \to 0} e^{x}}$

Step 2

Move the limit into the exponent.

$\frac{lim_{x \to 0} x}{e^{lim_{x \to 0} x}}$

Step 3

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 3.1

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

$\frac{0}{e^{lim_{x \to 0} x}}$

Step 3.2

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

$\frac{0}{e^{0}}$

Step 4

Simplify the answer.

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Step 4.1

Anything raised to $0$ is $1$ .

$\frac{0}{1}$

Step 4.2

Divide $0$ by $1$ .

$0$