Calculus Examples

$lim_{x \to - 4} \frac{{(x + 7)}^{4}}{x + 1}$

Step 1

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

$\frac{lim_{x \to - 4} {(x + 7)}^{4}}{lim_{x \to - 4} x + 1}$

Step 2

Move the exponent $4$ from ${(x + 7)}^{4}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to - 4} x + 7)}^{4}}{lim_{x \to - 4} x + 1}$

Step 3

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

$\frac{{(lim_{x \to - 4} x + lim_{x \to - 4} 7)}^{4}}{lim_{x \to - 4} x + 1}$

Step 4

Evaluate the limit of $7$ which is constant as $x$ approaches $- 4$ .

$\frac{{(lim_{x \to - 4} x + 7)}^{4}}{lim_{x \to - 4} x + 1}$

Step 5

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

$\frac{{(lim_{x \to - 4} x + 7)}^{4}}{lim_{x \to - 4} x + lim_{x \to - 4} 1}$

Step 6

Evaluate the limit of $1$ which is constant as $x$ approaches $- 4$ .

$\frac{{(lim_{x \to - 4} x + 7)}^{4}}{lim_{x \to - 4} x + 1}$

Step 7

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

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Step 7.1

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

$\frac{{(- 4 + 7)}^{4}}{lim_{x \to - 4} x + 1}$

Step 7.2

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

$\frac{{(- 4 + 7)}^{4}}{- 4 + 1}$

Step 8

Simplify the answer.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Add $- 4$ and $7$ .

$\frac{3^{4}}{- 4 + 1}$

Step 8.1.2

Raise $3$ to the power of $4$ .

$\frac{81}{- 4 + 1}$

Step 8.2

Add $- 4$ and $1$ .

$\frac{81}{- 3}$

Step 8.3

Divide $81$ by $- 3$ .

$- 27$