What is the limit as x approaches 0+of ((x-3))/(x^2) ?

The limit as x approaches 0+of ((x-3))/(x^2) is -infinity

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limit as x approaches 0+of ((x-3))/(x^2)

x \to 0 + lim (\frac{( x - 3 )}{x ^{2}})

- \infty

Solution steps

x \to 0 + lim (\frac{x - 3}{x ^{2}})

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

= x \to 0 + lim ((x - 3) \frac{1}{x ^{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 0 + lim (x - 3) \cdot x \to 0 + lim (\frac{1}{x ^{2}})

x \to 0 + lim (x - 3) = - 3

x \to 0 + lim (\frac{1}{x ^{2}}) = \infty

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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

x \to - 4 lim ((3 x + 2) (x - 2))

x \to 4 lim (2 x^{2} + 4 x + 1)

x \to 0 lim (ln (1 - e^{x}))

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

What is the limit as x approaches 0+of ((x-3))/(x^2) ?
The limit as x approaches 0+of ((x-3))/(x^2) is -infinity