Evaluate limit as x approaches 0 of x^2-2

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

Take the limit of each term.

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Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

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

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

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

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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

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

Evaluate the limit of $2$ which is constant as $x$ approaches $0$ .

$0^{2} - 2$

Simplify the answer.

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

$0 - 2$

Subtract $2$ from $0$ .

$- 2$

Evaluate limit as x approaches 0 of x^2-2

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