Calculus Examples

$\frac{lim_{W \to 8} 4 - 3 a^{3}}{a^{3} - 1}$

Step 1

Evaluate the limit of $4 - 3 a^{3}$ which is constant as $W$ approaches $8$ .

$\frac{4 - 3 a^{3}}{a^{3} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{3}$ .

$\frac{4 - 3 a^{3}}{a^{3} - 1^{3}}$

Step 2.2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = a$ and $b = 1$ .

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

Step 2.3

Simplify.

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Step 2.3.1

Multiply $a$ by $1$ .

$\frac{4 - 3 a^{3}}{(a - 1) (a^{2} + a + 1^{2})}$

Step 2.3.2

One to any power is one.

$\frac{4 - 3 a^{3}}{(a - 1) (a^{2} + a + 1)}$