Calculus Examples

$lim_{x \to 2} {(x^{2} - x)}^{5}$

Step 1

Move the exponent $5$ from ${(x^{2} - x)}^{5}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 2} x^{2} - x)}^{5}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

${(lim_{x \to 2} x^{2} - lim_{x \to 2} x)}^{5}$

Step 3

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

${({(lim_{x \to 2} x)}^{2} - lim_{x \to 2} x)}^{5}$

Step 4

Evaluate the limits by plugging in $2$ for all occurrences of $x$ .

Tap for more steps...

Step 4.1

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

${(2^{2} - lim_{x \to 2} x)}^{5}$

Step 4.2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

${(2^{2} - 2)}^{5}$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Raise $2$ to the power of $2$ .

${(4 - 2)}^{5}$

Step 5.2

Subtract $2$ from $4$ .

$2^{5}$

Step 5.3

Raise $2$ to the power of $5$ .

$32$