Calculus Examples

$lim_{x \to 5} \frac{x - 5}{(x - 5) (x + 5)}$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $x - 5$ .

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Step 1.1.1

Cancel the common factor.

$lim_{x \to 5} \frac{x - 5}{(x - 5) (x + 5)}$

Step 1.1.2

Rewrite the expression.

$lim_{x \to 5} \frac{1}{x + 5}$

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $5$ .

$\frac{lim_{x \to 5} 1}{lim_{x \to 5} x + 5}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $5$ .

$\frac{1}{lim_{x \to 5} x + 5}$

Step 1.4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$\frac{1}{lim_{x \to 5} x + lim_{x \to 5} 5}$

Step 1.5

Evaluate the limit of $5$ which is constant as $x$ approaches $5$ .

$\frac{1}{lim_{x \to 5} x + 5}$

Step 2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$\frac{1}{5 + 5}$

Step 3

Add $5$ and $5$ .

$\frac{1}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10}$

Decimal Form:

$0.1$