Calculus Examples

$lim_{x \to - 2} (4) (x^{2} + 4 x - 5)$

Step 1

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

$4 lim_{x \to - 2} x^{2} + 4 x - 5$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 2$ .

$4 (lim_{x \to - 2} x^{2} + lim_{x \to - 2} 4 x - lim_{x \to - 2} 5)$

Step 3

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

$4 ({(lim_{x \to - 2} x)}^{2} + lim_{x \to - 2} 4 x - lim_{x \to - 2} 5)$

Step 4

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

$4 ({(lim_{x \to - 2} x)}^{2} + 4 lim_{x \to - 2} x - lim_{x \to - 2} 5)$

Step 5

Evaluate the limit of $5$ which is constant as $x$ approaches $- 2$ .

$4 ({(lim_{x \to - 2} x)}^{2} + 4 lim_{x \to - 2} x - 1 \cdot 5)$

Step 6

Evaluate the limits by plugging in $- 2$ for all occurrences of $x$ .

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Step 6.1

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

$4 ({(- 2)}^{2} + 4 lim_{x \to - 2} x - 1 \cdot 5)$

Step 6.2

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

$4 ({(- 2)}^{2} + 4 \cdot - 2 - 1 \cdot 5)$

Step 7

Simplify the answer.

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Step 7.1

Simplify each term.

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Step 7.1.1

Raise $- 2$ to the power of $2$ .

$4 (4 + 4 \cdot - 2 - 1 \cdot 5)$

Step 7.1.2

Multiply $4$ by $- 2$ .

$4 (4 - 8 - 1 \cdot 5)$

Step 7.1.3

Multiply $- 1$ by $5$ .

$4 (4 - 8 - 5)$

Step 7.2

Subtract $8$ from $4$ .

$4 (- 4 - 5)$

Step 7.3

Subtract $5$ from $- 4$ .

$4 \cdot - 9$

Step 7.4

Multiply $4$ by $- 9$ .

$- 36$