Calculus Examples

$f (x) = 10^{2} \sin (\frac{1}{5 (10^{2})})$

Step 1

Raise $10$ to the power of $2$ .

$f (x) = 100 \sin (\frac{1}{5 (10^{2})})$

Step 2

Divide using scientific notation.

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Step 2.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$f (x) = 100 \sin ((\frac{1}{5}) (\frac{1}{10^{2}}))$

Step 2.2

Divide $1$ by $5$ .

$f (x) = 100 \sin (0.2 (\frac{1}{10^{2}}))$

Step 2.3

Move $10^{2}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$f (x) = 100 \sin (0.2 \cdot 10^{- 2})$

Step 3

Move the decimal point in $0.2$ to the right by $1$ place and decrease the power of $10^{- 2}$ by $1$ .

$f (x) = 100 \sin (2 \cdot 10^{- 3})$

Step 4

Evaluate $\sin (2 \cdot 10^{- 3})$ .

$f (x) = 100 \cdot 0.0000349$

Step 5

Multiply $100$ by $0.0000349$ .

$f (x) = 0.00349065$