Calculus Examples

$lim_{x \to 3} (x^{2}) + 4 x - \frac{21}{x - 3}$

Step 1

Combine terms.

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Step 1.1

To write $x^{2}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$lim_{x \to 3} 4 x + \frac{x^{2} (x - 3)}{x - 3} - \frac{21}{x - 3}$

Step 1.2

Combine the numerators over the common denominator.

$lim_{x \to 3} 4 x + \frac{x^{2} (x - 3) - 21}{x - 3}$

Step 1.3

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$lim_{x \to 3} \frac{4 x (x - 3)}{x - 3} + \frac{x^{2} (x - 3) - 21}{x - 3}$

Step 1.4

Combine the numerators over the common denominator.

$lim_{x \to 3} \frac{4 x (x - 3) + x^{2} (x - 3) - 21}{x - 3}$

Step 2

Since the function approaches $\infty$ from the left and $- \infty$ from the right, the limit does not exist.

$Does not exist$