Calculus Examples

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

Step 1

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

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

Step 2

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

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

Step 3

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

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

Step 4

Evaluate the limits by plugging in $- 2$ for all occurrences of $x$ .

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

${(- 2)}^{3} + {(- 2)}^{2} + 2$

Step 5

Simplify the answer.

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Step 5.1

Simplify each term.

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Step 5.1.1

Raise $- 2$ to the power of $3$ .

$- 8 + {(- 2)}^{2} + 2$

Step 5.1.2

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

$- 8 + 4 + 2$

Step 5.2

Add $- 8$ and $4$ .

$- 4 + 2$

Step 5.3

Add $- 4$ and $2$ .

$- 2$