What is the limit as x approaches 0-of (x^3+4)/(x^2) ?

The limit as x approaches 0-of (x^3+4)/(x^2) is infinity

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limit as x approaches 0-of (x^3+4)/(x^2)

x \to 0 - lim (\frac{x ^{3} + 4}{x ^{2}})

\infty

Solution steps

x \to 0 - lim (\frac{x ^{3} + 4}{x ^{2}})

Divide by highest denominator power:

x + \frac{4}{x ^{2}}

= x \to 0 - lim (x + \frac{4}{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 (x) + x \to 0 - lim (\frac{4}{x ^{2}})

x \to 0 - lim (x) = 0

x \to 0 - lim (\frac{4}{x ^{2}}) = \infty

= 0 + \infty

Apply Infinity Property:

c + \infty = \infty

= \infty

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

x \to 0 lim (6 sin (x))

x \to 2 lim (x^{5} + 2 x^{3} - x - 8)

x \to 0 + lim (x - 1)

x \to 3 lim (4 x - 6)

What is the limit as x approaches 0-of (x^3+4)/(x^2) ?
The limit as x approaches 0-of (x^3+4)/(x^2) is infinity