Calculus Examples

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

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

Step 1

Simplify the numerator.

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Step 1.1

Let

u = 1

$u = 1$ . Substitute

u

$u$ for all occurrences of

1

$1$ .

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Step 1.1.1

Subtract

2 u^{2}

$2 u^{2}$ from

2 u^{2}

$2 u^{2}$ .

\frac{4 h u + 2 h^{2} + 4 + 0 - 4}{h}

$\frac{4 h u + 2 h^{2} + 4 + 0 - 4}{h}$

Step 1.1.2

Add

4 h u + 2 h^{2} + 4

$4 h u + 2 h^{2} + 4$ and

0

$0$ .

\frac{4 h u + 2 h^{2} + 4 - 4}{h}

$\frac{4 h u + 2 h^{2} + 4 - 4}{h}$

Step 1.1.3

Subtract

4

$4$ from

4

$4$ .

\frac{4 h u + 2 h^{2} + 0}{h}

$\frac{4 h u + 2 h^{2} + 0}{h}$

Step 1.1.4

Add

4 h u + 2 h^{2}

$4 h u + 2 h^{2}$ and

0

$0$ .

\frac{4 h u + 2 h^{2}}{h}

$\frac{4 h u + 2 h^{2}}{h}$

\frac{4 h u + 2 h^{2}}{h}

$\frac{4 h u + 2 h^{2}}{h}$

Step 1.2

Factor

2 h

$2 h$ out of

4 h u + 2 h^{2}

$4 h u + 2 h^{2}$ .

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Step 1.2.1

Factor

2 h

$2 h$ out of

4 h u

$4 h u$ .

\frac{2 h (2 u) + 2 h^{2}}{h}

$\frac{2 h (2 u) + 2 h^{2}}{h}$

Step 1.2.2

Factor

2 h

$2 h$ out of

2 h^{2}

$2 h^{2}$ .

\frac{2 h (2 u) + 2 h (h)}{h}

$\frac{2 h (2 u) + 2 h (h)}{h}$

Step 1.2.3

Factor

2 h

$2 h$ out of

2 h (2 u) + 2 h (h)

$2 h (2 u) + 2 h (h)$ .

\frac{2 h (2 u + h)}{h}

$\frac{2 h (2 u + h)}{h}$

\frac{2 h (2 u + h)}{h}

$\frac{2 h (2 u + h)}{h}$

Step 1.3

Replace all occurrences of

u

$u$ with

1

$1$ .

\frac{2 h (2 \cdot 1 + h)}{h}

$\frac{2 h (2 \cdot 1 + h)}{h}$

Step 1.4

Multiply

2

$2$ by

1

$1$ .

\frac{2 h (2 + h)}{h}

$\frac{2 h (2 + h)}{h}$

\frac{2 h (2 + h)}{h}

$\frac{2 h (2 + h)}{h}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of

h

$h$ .

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Step 2.1.1

Cancel the common factor.

\frac{2 h (2 + h)}{h}

$\frac{2 h (2 + h)}{h}$

Step 2.1.2

Divide

2 (2 + h)

$2 (2 + h)$ by

1

$1$ .

2 (2 + h)

$2 (2 + h)$

2 (2 + h)

$2 (2 + h)$

Step 2.2

Apply the distributive property.

2 \cdot 2 + 2 h

$2 \cdot 2 + 2 h$

Step 2.3

Multiply

2

$2$ by

2

$2$ .

4 + 2 h

$4 + 2 h$

4 + 2 h

$4 + 2 h$

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

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

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$