Precalculus Examples

$lim_{x \to - 3} \sqrt[3]{10 + 3 x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt[3]{lim_{x \to - 3} 10 + 3 x}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 3$ .

$\sqrt[3]{lim_{x \to - 3} 10 + lim_{x \to - 3} 3 x}$

Step 1.3

Evaluate the limit of $10$ which is constant as $x$ approaches $- 3$ .

$\sqrt[3]{10 + lim_{x \to - 3} 3 x}$

Step 1.4

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\sqrt[3]{10 + 3 lim_{x \to - 3} x}$

Step 2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$\sqrt[3]{10 + 3 \cdot - 3}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $3$ by $- 3$ .

$\sqrt[3]{10 - 9}$

Step 3.2

Subtract $9$ from $10$ .

$\sqrt[3]{1}$

Step 3.3

Any root of $1$ is $1$ .

$1$