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

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

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

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

\infty

Solution steps

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

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

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

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

Simplify

\frac{x}{( x ( \frac{3}{x} - 1 ) ) ^{2}} : \frac{1}{\frac{9}{x} - 6 + x}

= x \to 3 + lim (\frac{1}{\frac{9}{x} - 6 + x})

For

x

approaching

3

from the right

, x > 3 \Rightarrow \frac{9}{x} - 6 + x > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

\frac{\partial}{\partial x} (x y + z (x + 2 y - 1))

x + y = 2, y = x^{2}

x \to 3 lim (\frac{x + 4}{x - 3})

y^{^{''}} - 8 y^{^{'}} + 52 y = 0

\int e^{- s t} 1 d t

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