Precalculus Examples

$lim_{x \to - 1} 1 - x^{2}$

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 $- 1$ .

$lim_{x \to - 1} 1 - lim_{x \to - 1} x^{2}$

Step 1.2

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

$1 - lim_{x \to - 1} x^{2}$

Step 1.3

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

$1 - {(lim_{x \to - 1} x)}^{2}$

Step 2

Evaluate the limit of $x$ by plugging in $- 1$ for $x$ .

$1 - {(- 1)}^{2}$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 3.1.1.1

Multiply $- 1$ by ${(- 1)}^{2}$ .

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Step 3.1.1.1.1

Raise $- 1$ to the power of $1$ .

$1 + {(- 1)}^{1} {(- 1)}^{2}$

Step 3.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 + {(- 1)}^{1 + 2}$

Step 3.1.1.2

Add $1$ and $2$ .

$1 + {(- 1)}^{3}$

Step 3.1.2

Raise $- 1$ to the power of $3$ .

$1 - 1$

Step 3.2

Subtract $1$ from $1$ .

$0$