Calculus Examples

$lim_{x \to 0} x^{3} + 3 x$

Step 1

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

$lim_{x \to 0} x^{3} + lim_{x \to 0} 3 x$

Step 2

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 0} x)}^{3} + lim_{x \to 0} 3 x$

Step 3

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

${(lim_{x \to 0} x)}^{3} + 3 lim_{x \to 0} x$

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 $x$ by plugging in $0$ for $x$ .

$0^{3} + 3 lim_{x \to 0} x$

Step 4.2

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

$0^{3} + 3 \cdot 0$

Step 5

Simplify the answer.

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Step 5.1

Simplify each term.

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Step 5.1.1

Raising $0$ to any positive power yields $0$ .

$0 + 3 \cdot 0$

Step 5.1.2

Multiply $3$ by $0$ .

$0 + 0$

Step 5.2

Add $0$ and $0$ .

$0$