Calculus Examples

$f (x) = \frac{\cos (2 x) - \cos (x)}{x^{2}}$ , $f (0.01)$

Step 1

Replace the variable $x$ with $0.01$ in the expression.

$f (0.01) = \frac{\cos (2 (0.01)) - \cos (0.01)}{{(0.01)}^{2}}$

Step 2

Simplify $\frac{\cos (2 (0.01)) - \cos (0.01)}{{(0.01)}^{2}}$ .

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Step 2.1

Remove parentheses.

$\frac{\cos (2 (0.01)) - \cos (0.01)}{{(0.01)}^{2}}$

Step 2.2

Multiply $2$ by $0.01$ .

$\frac{\cos (0.02) - \cos (0.01)}{{0.01}^{2}}$

Step 2.3

Raise $0.01$ to the power of $2$ .

$\frac{\cos (0.02) - \cos (0.01)}{0.0001}$

Step 2.4

Evaluate $\cos (0.02)$ .

$\frac{0.9998 - \cos (0.01)}{0.0001}$

Step 2.5

Evaluate $\cos (0.01)$ .

$\frac{0.9998 - 1 \cdot 0.99999998}{0.0001}$

Step 2.6

Multiply $- 1$ by $0.99999998$ .

$\frac{0.9998 - 0.99999998}{0.0001}$

Step 2.7

Subtract $0.99999998$ from $0.9998$ .

$\frac{- 0.00019997}{0.0001}$

Step 2.8

Divide $- 0.00019997$ by $0.0001$ .

$- 1.99978102$