Calculus Examples

$lim_{x \to 0} f (x) - g x$

Step 1

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

$lim_{x \to 0} f (x) - lim_{x \to 0} g x$

Step 2

Move the term $g$ outside of the limit because it is constant with respect to $x$ .

$lim_{x \to 0} f (x) - g lim_{x \to 0} x$

Step 3

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

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Step 3.1

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

$f (0) - g lim_{x \to 0} x$

Step 3.2

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

$f (0) - g \cdot 0$

Step 4

Simplify the answer.

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Step 4.1

Multiply $- g \cdot 0$ .

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Step 4.1.1

Multiply $0$ by $- 1$ .

$f (0) + 0 g$

Step 4.1.2

Multiply $0$ by $g$ .

$f (0) + 0$

Step 4.2

Add $f (0)$ and $0$ .

$f (0)$