Calculus Examples

$lim_{x \to - 2} (x + 3) (2 - x)$

Step 1

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

$lim_{x \to - 2} x + 3 \cdot lim_{x \to - 2} 2 - x$

Step 2

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

$(lim_{x \to - 2} x + lim_{x \to - 2} 3) \cdot lim_{x \to - 2} 2 - x$

Step 3

Evaluate the limit of $3$ which is constant as $x$ approaches $- 2$ .

$(lim_{x \to - 2} x + 3) \cdot lim_{x \to - 2} 2 - x$

Step 4

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

$(lim_{x \to - 2} x + 3) \cdot (lim_{x \to - 2} 2 - lim_{x \to - 2} x)$

Step 5

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

$(lim_{x \to - 2} x + 3) \cdot (2 - lim_{x \to - 2} x)$

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 $x$ .

$(- 2 + 3) \cdot (2 - lim_{x \to - 2} x)$

Step 6.2

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

$(- 2 + 3) \cdot (2 + 2)$

Step 7

Simplify the answer.

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Step 7.1

Add $- 2$ and $3$ .

$1 \cdot (2 + 2)$

Step 7.2

Multiply $2 + 2$ by $1$ .

$2 + 2$

Step 7.3

Add $2$ and $2$ .

$4$