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

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

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

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

\frac{1}{1 - \frac{3}{x}}

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

For

x

approaching

3

from the left

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

The denominator is a negative quantity approaching 0 from the left

= - (- \infty)

Simplify

= \infty

ln (A x^{4} + B)

x \to - 3 lim (∣ x - 1 ∣)

\frac{\partial}{\partial x} (- 7 e^{- 7 y} sin (7 x))

x^{2} + y^{2} = 64, - 8, 3

y^{^{''}} + 3 y = t^{3} - 1

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