Calculus Examples

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

Step 1

Split the limit using the Sum of Limits Rule on the limit as $h$ approaches $0$ .

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

Step 2

Evaluate the limit of $f x$ which is constant as $h$ approaches $0$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Add $x$ and $0$ .

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