Calculus Examples

$\frac{lim_{x \to 0} {(- 0.1)}^{3} + 4 {(- 0.1)}^{2}}{{(- 0.1)}^{2}}$

Step 1

Evaluate the limit of ${(- 0.1)}^{3} + 4 {(- 0.1)}^{2}$ which is constant as $x$ approaches $0$ .

$\frac{{(- 0.1)}^{3} + 4 {(- 0.1)}^{2}}{{(- 0.1)}^{2}}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Raise $- 0.1$ to the power of $3$ .

$\frac{- 0.001 + 4 {(- 0.1)}^{2}}{{(- 0.1)}^{2}}$

Step 2.1.2

Raise $- 0.1$ to the power of $2$ .

$\frac{- 0.001 + 4 \cdot 0.01}{{(- 0.1)}^{2}}$

Step 2.1.3

Multiply $4$ by $0.01$ .

$\frac{- 0.001 + 0.04}{{(- 0.1)}^{2}}$

Step 2.1.4

Add $- 0.001$ and $0.04$ .

$\frac{0.039}{{(- 0.1)}^{2}}$

Step 2.2

Raise $- 0.1$ to the power of $2$ .

$\frac{0.039}{0.01}$

Step 2.3

Divide $0.039$ by $0.01$ .

$3.9$