What is the limit as x approaches 1-of x/((x-1)^2) ?

The limit as x approaches 1-of x/((x-1)^2) is infinity

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limit as x approaches 1-of x/((x-1)^2)

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

\infty

Solution steps

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

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

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

x \to 1 - lim (x) = 1

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{d y}{d x} = \frac{3 x + 2}{y}

\int \frac{3}{y ^{2}} d y

\int e^{\frac{- l n ( 2 ) ( t )}{x}} d t

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

\frac{d}{d x} (- 4 x + 2)

What is the limit as x approaches 1-of x/((x-1)^2) ?
The limit as x approaches 1-of x/((x-1)^2) is infinity