What is the limit as x approaches-3+of (-5x)/(x+3) ?

The limit as x approaches-3+of (-5x)/(x+3) is infinity

limit as x approaches-3+of (-5x)/(x+3)

x \to - 3 + lim (\frac{- 5 x}{x + 3})

\infty

Solution steps

x \to - 3 + lim (\frac{- 5 x}{x + 3})

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

= - 5 \cdot x \to - 3 + lim (\frac{x}{x + 3})

Divide by highest denominator power:

\frac{1}{1 + \frac{3}{x}}

= - 5 \cdot x \to - 3 + lim (\frac{1}{1 + \frac{3}{x}})

For

x

approaching

- 3

from the right

, x > - 3 \Rightarrow 1 + \frac{3}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - 5 (- \infty)

Apply Infinity Property:

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

= \infty

\int_{0}^{1} x 3^{x} d x

2 x d y + y d x = 0

x y y^{^{'}} + 4 x^{2} + y^{2} = 0

2 x d z - 2 z d x = x^{2} + 4 z^{2} d x

\int \frac{1}{( x + 8 ) ( x ^{2} + 16 )} d x

What is the limit as x approaches-3+of (-5x)/(x+3) ?
The limit as x approaches-3+of (-5x)/(x+3) is infinity