Calculus Examples

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

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

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

Step 2

Evaluate the limit of $2$ which is constant as $x$ approaches $4$ .

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

Step 3

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

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

Step 4

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

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

Step 4.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$2 - 4 - 4^{2}$

Step 5

Simplify the answer.

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Step 5.1

Simplify each term.

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Step 5.1.1

Raise $4$ to the power of $2$ .

$2 - 4 - 1 \cdot 16$

Step 5.1.2

Multiply $- 1$ by $16$ .

$2 - 4 - 16$

Step 5.2

Subtract $4$ from $2$ .

$- 2 - 16$

Step 5.3

Subtract $16$ from $- 2$ .

$- 18$