Calculus Examples

$\frac{lim_{x \to - 3} 4 x^{3} + 1}{7 - 2 x^{2}}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{x \to - 3} 4 x^{3} + lim_{x \to - 3} 1}{7 - 2 x^{2}}$

Step 1.2

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$\frac{4 lim_{x \to - 3} x^{3} + lim_{x \to - 3} 1}{7 - 2 x^{2}}$

Step 1.3

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

$\frac{4 {(lim_{x \to - 3} x)}^{3} + lim_{x \to - 3} 1}{7 - 2 x^{2}}$

Step 1.4

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

$\frac{4 {(lim_{x \to - 3} x)}^{3} + 1}{7 - 2 x^{2}}$

Step 2

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

$\frac{4 {(- 3)}^{3} + 1}{7 - 2 x^{2}}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$\frac{4 \cdot - 27 + 1}{7 - 2 x^{2}}$

Step 3.1.2

Multiply $4$ by $- 27$ .

$\frac{- 108 + 1}{7 - 2 x^{2}}$

Step 3.1.3

Add $- 108$ and $1$ .

$\frac{- 107}{7 - 2 x^{2}}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{107}{7 - 2 x^{2}}$