What is the limit as x approaches 3+of (x^2)/(3x-9) ?

The limit as x approaches 3+of (x^2)/(3x-9) is infinity

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limit as x approaches 3+of (x^2)/(3x-9)

x \to 3 + lim (\frac{x ^{2}}{3 x - 9})

\infty

Solution steps

x \to 3 + lim (\frac{x ^{2}}{3 x - 9})

Factor out

3 x

from

3 x - 9 : 3 x (1 - \frac{9}{3 x})

= x \to 3 + lim (\frac{x ^{2}}{3 x ( 1 - \frac{9}{3 x} )})

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

= \frac{1}{3} \cdot x \to 3 + lim (\frac{x ^{2}}{x ( 1 - \frac{9}{3 x} )})

Simplify

\frac{x ^{2}}{x ( 1 - \frac{9}{3 x} )} : \frac{x ^{2}}{x - 3}

= \frac{1}{3} \cdot x \to 3 + lim (\frac{x ^{2}}{x - 3})

\frac{x ^{2}}{x - 3} = x^{2} \frac{1}{x - 3}

= \frac{1}{3} \cdot x \to 3 + lim (x^{2} \frac{1}{x - 3})

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

With the exception of indeterminate form

= \frac{1}{3} \cdot x \to 3 + lim (x^{2}) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (x^{2}) = 9

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

= \frac{1}{3} \cdot 9 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

- 2 x^{4} + 2 x^{3} - x^{2} + x

y = 7 e^{x}

\int \frac{1}{x ^{2} 4 x ^{2} + 49} d x

\int \frac{- x ^{2} - 1}{x ^{2} - 1} d x

What is the limit as x approaches 3+of (x^2)/(3x-9) ?
The limit as x approaches 3+of (x^2)/(3x-9) is infinity