Calculus Examples

$lim_{y \to 5} {(22 - y)}^{\frac{4}{3}}$

Step 1

Move the exponent $\frac{4}{3}$ from ${(22 - y)}^{\frac{4}{3}}$ outside the limit using the Limits Power Rule.

${(lim_{y \to 5} 22 - y)}^{\frac{4}{3}}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $y$ approaches $5$ .

${(lim_{y \to 5} 22 - lim_{y \to 5} y)}^{\frac{4}{3}}$

Step 3

Evaluate the limit of $22$ which is constant as $y$ approaches $5$ .

${(22 - lim_{y \to 5} y)}^{\frac{4}{3}}$

Step 4

Simplify the expression.

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Step 4.1

Evaluate the limit of $y$ by plugging in $5$ for $y$ .

${(22 - 5)}^{\frac{4}{3}}$

Step 4.2

Subtract $5$ from $22$ .

$17^{\frac{4}{3}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$17^{\frac{4}{3}}$

Decimal Form:

$43.71178704 \dots$