Calculus Examples

$lim_{x \to 0} x^{2} - 1$

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 $0$ .

$lim_{x \to 0} x^{2} - lim_{x \to 0} 1$

Step 1.2

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

${(lim_{x \to 0} x)}^{2} - lim_{x \to 0} 1$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

${(lim_{x \to 0} x)}^{2} - 1 \cdot 1$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$0^{2} - 1 \cdot 1$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raising $0$ to any positive power yields $0$ .

$0 - 1 \cdot 1$

Step 3.1.2

Multiply $- 1$ by $1$ .

$0 - 1$

Step 3.2

Subtract $1$ from $0$ .

$- 1$