Calculus Examples

$lim_{x \to 4} \sqrt[3]{\frac{7 x}{x - 3}}$

Step 1

Move the limit under the radical sign.

$\sqrt[3]{lim_{x \to 4} \frac{7 x}{x - 3}}$

Step 2

Move the term $7$ outside of the limit because it is constant with respect to $x$ .

$\sqrt[3]{7 lim_{x \to 4} \frac{x}{x - 3}}$

Step 3

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $4$ .

$\sqrt[3]{7 \frac{lim_{x \to 4} x}{lim_{x \to 4} x - 3}}$

Step 4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$\sqrt[3]{7 \frac{lim_{x \to 4} x}{lim_{x \to 4} x - lim_{x \to 4} 3}}$

Step 5

Evaluate the limit of $3$ which is constant as $x$ approaches $4$ .

$\sqrt[3]{7 \frac{lim_{x \to 4} x}{lim_{x \to 4} x - 1 \cdot 3}}$

Step 6

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 6.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$\sqrt[3]{7 \frac{4}{lim_{x \to 4} x - 1 \cdot 3}}$

Step 6.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$\sqrt[3]{7 \frac{4}{4 - 1 \cdot 3}}$

Step 7

Simplify the answer.

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Step 7.1

Combine $7$ and $\frac{4}{4 - 1 \cdot 3}$ .

$\sqrt[3]{\frac{7 \cdot 4}{4 - 1 \cdot 3}}$

Step 7.2

Multiply $- 1$ by $3$ .

$\sqrt[3]{\frac{7 \cdot 4}{4 - 3}}$

Step 7.3

Subtract $3$ from $4$ .

$\sqrt[3]{\frac{7 \cdot 4}{1}}$

Step 7.4

Divide $7 \cdot 4$ by $1$ .

$\sqrt[3]{7 \cdot 4}$

Step 7.5

Multiply $7$ by $4$ .

$\sqrt[3]{28}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{28}$

Decimal Form:

$3.03658897 \dots$