Calculus Examples

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

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

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

Step 2

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

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

Step 3

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

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

Step 3.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 - 4^{- 1}$

Step 4

Simplify the answer.

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Step 4.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 \cdot \frac{4}{4} - \frac{1}{4}$

Step 4.3

Combine $4$ and $\frac{4}{4}$ .

$\frac{4 \cdot 4}{4} - \frac{1}{4}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 1}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $4$ by $4$ .

$\frac{16 - 1}{4}$

Step 4.5.2

Subtract $1$ from $16$ .

$\frac{15}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{4}$

Decimal Form:

$3.75$