Calculus Examples

$lim_{y \to - 3} {(5 - y)}^{\frac{4}{3}}$

Step 1

Move the exponent $\frac{4}{3}$ from ${(5 - y)}^{\frac{4}{3}}$ outside the limit using the Limits Power Rule.

${(lim_{y \to - 3} 5 - y)}^{\frac{4}{3}}$

Step 2

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

${(lim_{y \to - 3} 5 - lim_{y \to - 3} y)}^{\frac{4}{3}}$

Step 3

Evaluate the limit of $5$ which is constant as $y$ approaches $- 3$ .

${(5 - lim_{y \to - 3} y)}^{\frac{4}{3}}$

Step 4

Simplify terms.

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Step 4.1

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

${(5 + 3)}^{\frac{4}{3}}$

Step 4.2

Simplify the answer.

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Step 4.2.1

Add $5$ and $3$ .

$8^{\frac{4}{3}}$

Step 4.2.2

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{\frac{4}{3}}$

Step 4.2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{3 (\frac{4}{3})}$

Step 4.2.4

Cancel the common factor of $3$ .

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Step 4.2.4.1

Cancel the common factor.

$2^{3 (\frac{4}{3})}$

Step 4.2.4.2

Rewrite the expression.

$2^{4}$

Step 4.2.5

Raise $2$ to the power of $4$ .

$16$