Calculus Examples

$lim_{x \to 0} 1 - \frac{x^{2}}{6}$

Step 1

Evaluate the limit.

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Step 1.1

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

$lim_{x \to 0} 1 - lim_{x \to 0} \frac{x^{2}}{6}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$1 - lim_{x \to 0} \frac{x^{2}}{6}$

Step 1.3

Move the term $\frac{1}{6}$ outside of the limit because it is constant with respect to $x$ .

$1 - \frac{1}{6} lim_{x \to 0} x^{2}$

Step 1.4

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

$1 - \frac{1}{6} {(lim_{x \to 0} x)}^{2}$

Step 2

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

$1 - \frac{1}{6} \cdot 0^{2}$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

$1 - \frac{1}{6} \cdot 0$

Step 3.1.2

Multiply $- \frac{1}{6} \cdot 0$ .

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Step 3.1.2.1

Multiply $0$ by $- 1$ .

$1 + 0 (\frac{1}{6})$

Step 3.1.2.2

Multiply $0$ by $\frac{1}{6}$ .

$1 + 0$

Step 3.2

Add $1$ and $0$ .

$1$