Calculus Examples

$\frac{lim_{x \to o} x^{2} + 3 x}{x}$

Step 1

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

$\frac{lim_{x \to o} x^{2} + lim_{x \to o} 3 x}{x}$

Step 2

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to o} x)}^{2} + lim_{x \to o} 3 x}{x}$

Step 3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{{(lim_{x \to o} x)}^{2} + 3 lim_{x \to o} x}{x}$

Step 4

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

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Step 4.1

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

$\frac{o^{2} + 3 lim_{x \to o} x}{x}$

Step 4.2

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

$\frac{o^{2} + 3 o}{x}$

Step 5

Factor $o$ out of $o^{2} + 3 o$ .

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Step 5.1

Factor $o$ out of $o^{2}$ .

$\frac{o \cdot o + 3 o}{x}$

Step 5.2

Factor $o$ out of $3 o$ .

$\frac{o \cdot o + o \cdot 3}{x}$

Step 5.3

Factor $o$ out of $o \cdot o + o \cdot 3$ .

$\frac{o (o + 3)}{x}$