Calculus Examples

$lim_{x \to 0} \frac{f (x)}{f (x) + 2}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f (x)}{lim_{x \to 0} f (x) + 2}$

Step 2

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

$\frac{lim_{x \to 0} f (x)}{lim_{x \to 0} f (x) + lim_{x \to 0} 2}$

Step 3

Evaluate the limit of $2$ which is constant as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f (x)}{lim_{x \to 0} f (x) + 2}$

Step 4

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

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Step 4.1

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

$\frac{f (0)}{lim_{x \to 0} f (x) + 2}$

Step 4.2

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

$\frac{f (0)}{f (0) + 2}$