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}})

Divide by highest denominator power:

\frac{1}{x} + \frac{3}{x ^{2}}

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= \infty + \infty

Apply Infinity Property:

\infty + \infty = \infty

= \infty

ln (\frac{5 x ^{2} + x + 6}{x ^{3}})

\int 8 x - cos (x) d x

\frac{d}{d x} (2 cos (x))

\frac{d}{d x} ((sin (x^{2}) + x^{2}) (cos (x) - 3 x))

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