Calculus Examples

$\frac{lim_{x \to 0} 1}{x^{2}} \cdot (\frac{\sin (x)}{\sinh (x)} - 1)$

Step 1

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$\frac{1}{x^{2}} \cdot (\frac{\sin (x)}{\sinh (x)} - 1)$

Step 2

Simplify the answer.

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Step 2.1

Apply the distributive property.

$\frac{1}{x^{2}} \cdot \frac{\sin (x)}{\sinh (x)} + \frac{1}{x^{2}} \cdot - 1$

Step 2.2

Combine.

$\frac{1 \sin (x)}{x^{2} \sinh (x)} + \frac{1}{x^{2}} \cdot - 1$

Step 2.3

Combine $\frac{1}{x^{2}}$ and $- 1$ .

$\frac{1 \sin (x)}{x^{2} \sinh (x)} + \frac{- 1}{x^{2}}$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply $\sin (x)$ by $1$ .

$\frac{\sin (x)}{x^{2} \sinh (x)} + \frac{- 1}{x^{2}}$

Step 2.4.2

Move the negative in front of the fraction.

$\frac{\sin (x)}{x^{2} \sinh (x)} - \frac{1}{x^{2}}$