Calculus Examples

$\frac{lim_{h \to 0} (2 {(x + h)}^{2} - 5 (x + h) - 4) - (2 x^{2} - 5 x - 4)}{h}$

Step 1

Evaluate the limits by plugging in $0$ for all occurrences of $h$ .

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Step 1.1

Evaluate the limit of $(2 {(x + h)}^{2} - 5 (x + h) - 4) - (2 x^{2} - 5 x - 4)$ by plugging in $0$ for $h$ .

$\frac{2 {(x + 0)}^{2} - 5 (x + 0) - 4 - (2 x^{2} - 5 x - 4)}{h}$

Step 1.2

Combine the opposite terms in $2 {(x + 0)}^{2} - 5 (x + 0) - 4 - (2 x^{2} - 5 x - 4)$ .

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Step 1.2.1

Add $x$ and $0$ .

$\frac{2 x^{2} - 5 (x + 0) - 4 - (2 x^{2} - 5 x - 4)}{h}$

Step 1.2.2

Add $x$ and $0$ .

$\frac{2 x^{2} - 5 x - 4 - (2 x^{2} - 5 x - 4)}{h}$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{2 x^{2} - 5 x - 4 - (2 x^{2}) - (- 5 x) - - 4}{h}$

Step 1.3.2

Simplify.

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Step 1.3.2.1

Multiply $2$ by $- 1$ .

$\frac{2 x^{2} - 5 x - 4 - 2 x^{2} - (- 5 x) - - 4}{h}$

Step 1.3.2.2

Multiply $- 5$ by $- 1$ .

$\frac{2 x^{2} - 5 x - 4 - 2 x^{2} + 5 x - - 4}{h}$

Step 1.3.2.3

Multiply $- 1$ by $- 4$ .

$\frac{2 x^{2} - 5 x - 4 - 2 x^{2} + 5 x + 4}{h}$

Step 1.4

Combine the opposite terms in $2 x^{2} - 5 x - 4 - 2 x^{2} + 5 x + 4$ .

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Step 1.4.1

Subtract $2 x^{2}$ from $2 x^{2}$ .

$\frac{- 5 x - 4 + 0 + 5 x + 4}{h}$

Step 1.4.2

Add $- 5 x - 4$ and $0$ .

$\frac{- 5 x - 4 + 5 x + 4}{h}$

Step 1.4.3

Add $- 5 x$ and $5 x$ .

$\frac{0 - 4 + 4}{h}$

Step 1.4.4

Subtract $4$ from $0$ .

$\frac{- 4 + 4}{h}$

Step 1.4.5

Add $- 4$ and $4$ .

$\frac{0}{h}$

Step 2

Divide $0$ by $h$ .

$0$