Calculus Examples

$lim_{x \to - 17} {(x + 10)}^{\frac{2}{3}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the exponent $\frac{2}{3}$ from ${(x + 10)}^{\frac{2}{3}}$ outside the limit using the Limits Power Rule.

${(lim_{x \to - 17} x + 10)}^{\frac{2}{3}}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 17$ .

${(lim_{x \to - 17} x + lim_{x \to - 17} 10)}^{\frac{2}{3}}$

Step 1.3

Evaluate the limit of $10$ which is constant as $x$ approaches $- 17$ .

${(lim_{x \to - 17} x + 10)}^{\frac{2}{3}}$

Step 2

Evaluate the limit of $x$ by plugging in $- 17$ for $x$ .

${(- 17 + 10)}^{\frac{2}{3}}$

Step 3

Add $- 17$ and $10$ .

${(- 7)}^{\frac{2}{3}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

${(- 7)}^{\frac{2}{3}}$

Decimal Form:

$3.65930571 \dots$