Calculus Examples

$lim_{x \to 1} {(x^{2} - 4 x)}^{3}$

Step 1

Move the exponent $3$ from ${(x^{2} - 4 x)}^{3}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 1} x^{2} - 4 x)}^{3}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

${(lim_{x \to 1} x^{2} - lim_{x \to 1} 4 x)}^{3}$

Step 3

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

${({(lim_{x \to 1} x)}^{2} - lim_{x \to 1} 4 x)}^{3}$

Step 4

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

${({(lim_{x \to 1} x)}^{2} - 4 lim_{x \to 1} x)}^{3}$

Step 5

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

${(1^{2} - 4 lim_{x \to 1} x)}^{3}$

Step 5.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

${(1^{2} - 4 \cdot 1)}^{3}$

Step 6

Simplify the answer.

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Step 6.1

Simplify each term.

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Step 6.1.1

One to any power is one.

${(1 - 4 \cdot 1)}^{3}$

Step 6.1.2

Multiply $- 4$ by $1$ .

${(1 - 4)}^{3}$

Step 6.2

Subtract $4$ from $1$ .

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

Step 6.3

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

$- 27$