Calculus Examples

$\frac{lim_{x \to a} (5 - 4 x + 3 x^{2}) - (5 - 4 a + 3 a^{2})}{x - a}$

Step 1

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

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Step 1.1

Evaluate the limit of $(5 - 4 x + 3 x^{2}) - (5 - 4 a + 3 a^{2})$ by plugging in $a$ for $x$ .

$\frac{5 - 4 a + 3 a^{2} - (5 - 4 a + 3 a^{2})}{x - a}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{5 - 4 a + 3 a^{2} - 1 \cdot 5 - (- 4 a) - (3 a^{2})}{x - a}$

Step 1.2.2

Simplify.

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Step 1.2.2.1

Multiply $- 1$ by $5$ .

$\frac{5 - 4 a + 3 a^{2} - 5 - (- 4 a) - (3 a^{2})}{x - a}$

Step 1.2.2.2

Multiply $- 4$ by $- 1$ .

$\frac{5 - 4 a + 3 a^{2} - 5 + 4 a - (3 a^{2})}{x - a}$

Step 1.2.2.3

Multiply $3$ by $- 1$ .

$\frac{5 - 4 a + 3 a^{2} - 5 + 4 a - 3 a^{2}}{x - a}$

Step 1.3

Combine the opposite terms in $5 - 4 a + 3 a^{2} - 5 + 4 a - 3 a^{2}$ .

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Step 1.3.1

Subtract $5$ from $5$ .

$\frac{- 4 a + 3 a^{2} + 0 + 4 a - 3 a^{2}}{x - a}$

Step 1.3.2

Add $- 4 a + 3 a^{2}$ and $0$ .

$\frac{- 4 a + 3 a^{2} + 4 a - 3 a^{2}}{x - a}$

Step 1.3.3

Add $- 4 a$ and $4 a$ .

$\frac{3 a^{2} + 0 - 3 a^{2}}{x - a}$

Step 1.3.4

Add $3 a^{2}$ and $0$ .

$\frac{3 a^{2} - 3 a^{2}}{x - a}$

Step 1.3.5

Subtract $3 a^{2}$ from $3 a^{2}$ .

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

Step 2

Divide $0$ by $x - a$ .

$0$