Calculus Examples

$lim_{x \to 0} {(2 x - 1)}^{3}$

Step 1

Evaluate the limit.

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Step 1.1

Move the exponent $3$ from ${(2 x - 1)}^{3}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 0} 2 x - 1)}^{3}$

Step 1.2

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

${(lim_{x \to 0} 2 x - lim_{x \to 0} 1)}^{3}$

Step 1.3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

${(2 lim_{x \to 0} x - lim_{x \to 0} 1)}^{3}$

Step 1.4

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

${(2 lim_{x \to 0} x - 1 \cdot 1)}^{3}$

Step 2

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

${(2 \cdot 0 - 1 \cdot 1)}^{3}$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $0$ .

${(0 - 1 \cdot 1)}^{3}$

Step 3.1.2

Multiply $- 1$ by $1$ .

${(0 - 1)}^{3}$

Step 3.2

Subtract $1$ from $0$ .

${(- 1)}^{3}$

Step 3.3

Raise $- 1$ to the power of $3$ .

$- 1$