Calculus Examples

\frac{lim_{h \to 0} f (x + h) - f x}{h}

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

Step 1

Split the limit using the Sum of Limits Rule on the limit as

h

$h$ approaches

0

$0$ .

\frac{lim_{h \to 0} f (x + h) - lim_{h \to 0} f x}{h}

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

Step 2

Evaluate the limit of

f x

$f x$ which is constant as

h

$h$ approaches

0

$0$ .

\frac{lim_{h \to 0} f (x + h) - f x}{h}

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

Step 3

Evaluate the limits by plugging in

0

$0$ for all occurrences of

h

$h$ .

Tap for more steps...

Step 3.1

Evaluate the limit of

f (x + h)

$f (x + h)$ by plugging in

0

$0$ for

h

$h$ .

\frac{f (x + 0) - f x}{h}

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

Step 3.2

Add

x

$x$ and

0

$0$ .

\frac{f (x) - f x}{h}

$\frac{f (x) - f x}{h}$

\frac{f (x) - f x}{h}

$\frac{f (x) - f x}{h}$

\frac{lim_{h \to 0} (f (x + h) - f x)}{h}

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

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