Calculus Examples

$lim_{x \to 3} \frac{699}{{(x + 1)}^{0.94}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $699$ outside of the limit because it is constant with respect to $x$ .

$699 lim_{x \to 3} \frac{1}{{(x + 1)}^{0.94}}$

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $3$ .

$699 \frac{lim_{x \to 3} 1}{lim_{x \to 3} {(x + 1)}^{0.94}}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $3$ .

$699 \frac{1}{lim_{x \to 3} {(x + 1)}^{0.94}}$

Step 1.4

Move the exponent $0.94$ from ${(x + 1)}^{0.94}$ outside the limit using the Limits Power Rule.

$699 \frac{1}{{(lim_{x \to 3} x + 1)}^{0.94}}$

Step 1.5

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

$699 \frac{1}{{(lim_{x \to 3} x + lim_{x \to 3} 1)}^{0.94}}$

Step 1.6

Evaluate the limit of $1$ which is constant as $x$ approaches $3$ .

$699 \frac{1}{{(lim_{x \to 3} x + 1)}^{0.94}}$

Step 2

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$699 \frac{1}{{(3 + 1)}^{0.94}}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Add $3$ and $1$ .

$699 \frac{1}{4^{0.94}}$

Step 3.1.2

Raise $4$ to the power of $0.94$ .

$699 (\frac{1}{3.6807506})$

Step 3.2

Divide $1$ by $3.6807506$ .

$699 \cdot 0.27168371$

Step 3.3

Multiply $699$ by $0.27168371$ .

$189.90691722$