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 right

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

The denominator is a positive quantity approaching 0 from the right

= - \infty

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

\int 13 tan^{4} (x) sec^{6} (x) d x

t an g e n t \frac{6 x}{x + 5}

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

\int e^{(- 3 x)} d x

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