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

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