Calculus Examples

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

Step 1

Set up the limit as a left-sided limit.

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

Step 2

Evaluate the limits by plugging in the value for the variable.

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Step 2.1

Evaluate the limit of $\frac{f (x + h) - f (x)}{h}$ by plugging in $0$ for $h$ .

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

Step 2.2

Since $\frac{f (x + 0) - f (x)}{0}$ is undefined, the limit does not exist.

$Does not exist$

Step 3

Set up the limit as a right-sided limit.

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

Step 4

Evaluate the limits by plugging in the value for the variable.

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Step 4.1

Evaluate the limit of $\frac{f (x + h) - f (x)}{h}$ by plugging in $0$ for $h$ .

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

Step 4.2

Since $\frac{f (x + 0) - f (x)}{0}$ is undefined, the limit does not exist.

$Does not exist$

Step 5

If either of the one-sided limits does not exist, the limit does not exist.

$Does not exist$