Calculus Examples

1 + (\frac{1}{2}) (0.1234) + \frac{{((\frac{- 1}{4}) (0.1234))}^{2}}{2!}

$1 + (\frac{1}{2}) (0.1234) + \frac{{((\frac{- 1}{4}) (0.1234))}^{2}}{2!}$

Step 1

Simplify each term.

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Step 1.1

Combine

$\frac{1}{2}$ and

$0.1234$ .

$1 + \frac{0.1234}{2} + \frac{{((\frac{- 1}{4}) (0.1234))}^{2}}{2!}$

Step 1.2

Divide

$0.1234$ by

$2$ .

$1 + 0.0617 + \frac{{((\frac{- 1}{4}) (0.1234))}^{2}}{2!}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Move the negative in front of the fraction.

$1 + 0.0617 + \frac{{(- \frac{1}{4} \cdot 0.1234)}^{2}}{2!}$

Step 1.3.2

Combine exponents.

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Step 1.3.2.1

Multiply

$0.1234$ by

$- 1$ .

$1 + 0.0617 + \frac{{(- 0.1234 (\frac{1}{4}))}^{2}}{2!}$

Step 1.3.2.2

Combine

$- 0.1234$ and

$\frac{1}{4}$ .

$1 + 0.0617 + \frac{{(\frac{- 0.1234}{4})}^{2}}{2!}$

Step 1.3.3

Apply the product rule to

$\frac{- 0.1234}{4}$ .

$1 + 0.0617 + \frac{\frac{{(- 0.1234)}^{2}}{4^{2}}}{2!}$

Step 1.3.4

Raise

$- 0.1234$ to the power of

$2$ .

$1 + 0.0617 + \frac{\frac{0.01522756}{4^{2}}}{2!}$

Step 1.3.5

Raise

$4$ to the power of

$2$ .

$1 + 0.0617 + \frac{\frac{0.01522756}{16}}{2!}$

Step 1.3.6

Divide

$0.01522756$ by

$16$ .

$1 + 0.0617 + \frac{0.00095172}{2!}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Expand

$2!$ to

$2 \cdot 1$ .

$1 + 0.0617 + \frac{0.00095172}{2 \cdot 1}$

Step 1.4.2

Multiply

$2$ by

$1$ .

$1 + 0.0617 + \frac{0.00095172}{2}$

Step 1.5

Divide

$0.00095172$ by

$2$ .

$1 + 0.0617 + 0.00047586$

Step 2

Simplify by adding numbers.

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Step 2.1

Add

$1$ and

$0.0617$ .

$1.0617 + 0.00047586$

Step 2.2

Add

$1.0617$ and

$0.00047586$ .

$1.06217586$