Calculus Examples

$\frac{lim_{x \to y} {(x)}^{3} - y^{3}}{x - y}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\frac{lim_{x \to y} {(x)}^{3} - lim_{x \to y} y^{3}}{x - y}$

Step 1.2

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

$\frac{{(lim_{x \to y} x)}^{3} - lim_{x \to y} y^{3}}{x - y}$

Step 1.3

Evaluate the limit of $y^{3}$ which is constant as $x$ approaches $y$ .

$\frac{{(lim_{x \to y} x)}^{3} - y^{3}}{x - y}$

Step 2

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

$\frac{y^{3} - y^{3}}{x - y}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Subtract $y^{3}$ from $y^{3}$ .

$\frac{0}{x - y}$

Step 3.2

Divide $0$ by $x - y$ .

$0$