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 right

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

The denominator is a negative quantity approaching 0 from the left

= 2 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\frac{\partial}{\partial x} (\frac{( 1 + y )}{( 1 + x )})

2 e^{t}

x \to 1 + lim (\frac{x ^{2}}{1 - x})

\int x e^{- x} d x

\int cos (x) e^{- x} d 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