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

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

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

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

\infty

Solution steps

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

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

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

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

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

x \to 3 - lim (x) = 3

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

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 - lim (ln (x^{2}))

x \to 0 lim (\frac{x}{2 x - 1})

x \to 0 - lim (x^{2} - k e^{- x})

x \to 0 + lim ((\frac{1}{3})^{\frac{1}{x}} + 1)

x \to 0 lim (\frac{( 1 - cos ( x ) )}{7 x \cdot sin ( x )})

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