Calculus Examples

$lim_{x \to 1} \frac{4}{x^{2 - 1}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$4 lim_{x \to 1} \frac{1}{x^{2 - 1}}$

Step 1.2

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

$4 \frac{lim_{x \to 1} 1}{lim_{x \to 1} x^{2 - 1}}$

Step 1.3

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

$4 \frac{1}{lim_{x \to 1} x^{2 - 1}}$

Step 1.4

Move the exponent $2 - 1$ from $x^{2 - 1}$ outside the limit using the Limits Power Rule.

$4 \frac{1}{{(lim_{x \to 1} x)}^{2 - 1}}$

Step 2

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

$4 \frac{1}{1^{2 - 1}}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Subtract $1$ from $2$ .

$4 \frac{1}{1^{1}}$

Step 3.1.2

Evaluate the exponent.

$4 (\frac{1}{1})$

Step 3.2

Cancel the common factor of $1$ .

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Step 3.2.1

Cancel the common factor.

$4 (\frac{1}{1})$

Step 3.2.2

Rewrite the expression.

$4 \cdot 1$

Step 3.3

Multiply $4$ by $1$ .

$4$