Calculus Examples

$lim_{x \to 1} e^{x^{3} - x}$

Step 1

Move the limit into the exponent.

$e^{lim_{x \to 1} x^{3} - x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$e^{lim_{x \to 1} x^{3} - lim_{x \to 1} x}$

Step 3

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

$e^{{(lim_{x \to 1} x)}^{3} - lim_{x \to 1} x}$

Step 4

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$e^{1^{3} - lim_{x \to 1} x}$

Step 4.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$e^{1^{3} - 1}$

Step 5

Simplify the answer.

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Step 5.1

One to any power is one.

$e^{1 - 1}$

Step 5.2

Subtract $1$ from $1$ .

$e^{0}$

Step 5.3

Anything raised to $0$ is $1$ .

$1$