Calculus Examples

$\frac{lim_{x \to - 10} 9 x + 90}{| x + 10 |}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 10$ .

$\frac{lim_{x \to - 10} 9 x + lim_{x \to - 10} 90}{| x + 10 |}$

Step 1.2

Move the term $9$ outside of the limit because it is constant with respect to $x$ .

$\frac{9 lim_{x \to - 10} x + lim_{x \to - 10} 90}{| x + 10 |}$

Step 1.3

Evaluate the limit of $90$ which is constant as $x$ approaches $- 10$ .

$\frac{9 lim_{x \to - 10} x + 90}{| x + 10 |}$

Step 2

Evaluate the limit of $x$ by plugging in $- 10$ for $x$ .

$\frac{9 \cdot - 10 + 90}{| x + 10 |}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $9$ by $- 10$ .

$\frac{- 90 + 90}{| x + 10 |}$

Step 3.1.2

Add $- 90$ and $90$ .

$\frac{0}{| x + 10 |}$

Step 3.2

Divide $0$ by $| x + 10 |$ .

$0$