Precalculus Examples

$lim_{x \to 3} \frac{15}{x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $15$ outside of the limit because it is constant with respect to $x$ .

$15 lim_{x \to 3} \frac{1}{x}$

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $3$ .

$15 \frac{lim_{x \to 3} 1}{lim_{x \to 3} x}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $3$ .

$15 \frac{1}{lim_{x \to 3} x}$

Step 2

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$15 (\frac{1}{3})$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $15$ .

$3 (5) \frac{1}{3}$

Step 3.2

Cancel the common factor.

$3 \cdot 5 \frac{1}{3}$

Step 3.3

Rewrite the expression.

$5$