Calculus Examples

$lim_{x \to 2} \sqrt[3]{10 x + 7}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt[3]{lim_{x \to 2} 10 x + 7}$

Step 1.2

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

$\sqrt[3]{lim_{x \to 2} 10 x + lim_{x \to 2} 7}$

Step 1.3

Move the term $10$ outside of the limit because it is constant with respect to $x$ .

$\sqrt[3]{10 lim_{x \to 2} x + lim_{x \to 2} 7}$

Step 1.4

Evaluate the limit of $7$ which is constant as $x$ approaches $2$ .

$\sqrt[3]{10 lim_{x \to 2} x + 7}$

Step 2

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

$\sqrt[3]{10 \cdot 2 + 7}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $10$ by $2$ .

$\sqrt[3]{20 + 7}$

Step 3.2

Add $20$ and $7$ .

$\sqrt[3]{27}$

Step 3.3

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3}}$

Step 3.4

Pull terms out from under the radical, assuming real numbers.

$3$