Calculus Examples

$lim_{x \to 2^{+}} \frac{14}{8 - 4 x}$

Step 1

Cancel the common factor of $14$ and $8 - 4 x$ .

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Step 1.1

Factor $2$ out of $14$ .

$lim_{x \to 2^{+}} \frac{2 (7)}{8 - 4 x}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $8$ .

$lim_{x \to 2^{+}} \frac{2 \cdot 7}{2 \cdot 4 - 4 x}$

Step 1.2.2

Factor $2$ out of $- 4 x$ .

$lim_{x \to 2^{+}} \frac{2 \cdot 7}{2 \cdot 4 + 2 (- 2 x)}$

Step 1.2.3

Factor $2$ out of $2 (4) + 2 (- 2 x)$ .

$lim_{x \to 2^{+}} \frac{2 \cdot 7}{2 (4 - 2 x)}$

Step 1.2.4

Cancel the common factor.

$lim_{x \to 2^{+}} \frac{2 \cdot 7}{2 (4 - 2 x)}$

Step 1.2.5

Rewrite the expression.

$lim_{x \to 2^{+}} \frac{7}{4 - 2 x}$

Step 2

Since the numerator is positive and the denominator $4 - 2 x$ approaches zero and is less than zero for $x$ near $2$ to the right, the function decreases without bound.

$- \infty$