Calculus Examples

$lim_{x \to 3} \frac{4 x^{2}}{2 x^{2}} - \frac{5 x}{3 x} - \frac{21}{9}$

Step 1

Reduce.

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Step 1.1

Cancel the common factor of $4$ and $2$ .

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Step 1.1.1

Factor $2$ out of $4 x^{2}$ .

$lim_{x \to 3} \frac{2 (2 x^{2})}{2 x^{2}} - \frac{5 x}{3 x} - \frac{21}{9}$

Step 1.1.2

Cancel the common factor.

$lim_{x \to 3} \frac{2 (2 x^{2})}{2 x^{2}} - \frac{5 x}{3 x} - \frac{21}{9}$

Step 1.1.3

Rewrite the expression.

$lim_{x \to 3} 2 - \frac{5 x}{3 x} - \frac{21}{9}$

Step 1.2

Cancel the common factor of $x$ .

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Step 1.2.1

Cancel the common factor.

$lim_{x \to 3} 2 - \frac{5 x}{3 x} - \frac{21}{9}$

Step 1.2.2

Rewrite the expression.

$lim_{x \to 3} 2 - \frac{5}{3} - \frac{21}{9}$

Step 1.3

Cancel the common factor of $21$ and $9$ .

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Step 1.3.1

Factor $3$ out of $21$ .

$lim_{x \to 3} 2 - \frac{5}{3} - \frac{3 (7)}{9}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $3$ out of $9$ .

$lim_{x \to 3} 2 - \frac{5}{3} - \frac{3 \cdot 7}{3 \cdot 3}$

Step 1.3.2.2

Cancel the common factor.

$lim_{x \to 3} 2 - \frac{5}{3} - \frac{3 \cdot 7}{3 \cdot 3}$

Step 1.3.2.3

Rewrite the expression.

$lim_{x \to 3} 2 - \frac{5}{3} - \frac{7}{3}$

Step 2

Evaluate the limit of $2 - \frac{5}{3} - \frac{7}{3}$ which is constant as $x$ approaches $3$ .

$2 - \frac{5}{3} - \frac{7}{3}$

Step 3

Simplify the answer.

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Step 3.1

Combine the numerators over the common denominator.

$2 + \frac{- 5 - 7}{3}$

Step 3.2

Subtract $7$ from $- 5$ .

$2 + \frac{- 12}{3}$

Step 3.3

Divide $- 12$ by $3$ .

$2 - 4$

Step 3.4

Subtract $4$ from $2$ .

$- 2$