What is the limit as x approaches-6-of (2x)/(6+x) ?

The limit as x approaches-6-of (2x)/(6+x) is infinity

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limit as x approaches-6-of (2x)/(6+x)

x \to - 6 - lim (\frac{2 x}{6 + x})

\infty

Solution steps

x \to - 6 - lim (\frac{2 x}{6 + x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to - 6 - lim (\frac{x}{6 + x})

Divide by highest denominator power:

\frac{1}{\frac{6}{x} + 1}

= 2 \cdot x \to - 6 - lim (\frac{1}{\frac{6}{x} + 1})

For

x

approaching

- 6

from the left

, x < - 6 \Rightarrow \frac{6}{x} + 1 > 0

The denominator is a positive quantity approaching 0 from the right

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

u \to - 2 lim (\frac{u + 2}{u ^{3} + 8})

t \to 0 + lim ((sin (t))^{t})

x \to 0 lim (+ (cos (2 x)) \frac{1}{x})

x \to 0 lim (\frac{1}{x} ln (x))

x \to 0 lim (\frac{( sin ( 5 x ) )}{sin ( 4 x )})

What is the limit as x approaches-6-of (2x)/(6+x) ?
The limit as x approaches-6-of (2x)/(6+x) is infinity