Calculus Examples

$\frac{lim_{h \to 0} (3 x - 2 + h) - (3 x - 2)}{h}$

Step 1

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

Tap for more steps...

Step 1.1

Evaluate the limit of $(3 x - 2 + h) - (3 x - 2)$ by plugging in $0$ for $h$ .

$\frac{3 x - 2 + 0 - (3 x - 2)}{h}$

Step 1.2

Add $3 x - 2$ and $0$ .

$\frac{3 x - 2 - (3 x - 2)}{h}$

Step 1.3

Simplify each term.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$\frac{3 x - 2 - (3 x) - - 2}{h}$

Step 1.3.2

Multiply $3$ by $- 1$ .

$\frac{3 x - 2 - 3 x - - 2}{h}$

Step 1.3.3

Multiply $- 1$ by $- 2$ .

$\frac{3 x - 2 - 3 x + 2}{h}$

Step 1.4

Combine the opposite terms in $3 x - 2 - 3 x + 2$ .

Tap for more steps...

Step 1.4.1

Subtract $3 x$ from $3 x$ .

$\frac{0 - 2 + 2}{h}$

Step 1.4.2

Subtract $2$ from $0$ .

$\frac{- 2 + 2}{h}$

Step 1.4.3

Add $- 2$ and $2$ .

$\frac{0}{h}$

Step 2

Divide $0$ by $h$ .

$0$