What is the limit as x approaches 0-of (x-1)/(x^2) ?

The limit as x approaches 0-of (x-1)/(x^2) is -infinity

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limit as x approaches 0-of (x-1)/(x^2)

x \to 0 - lim (\frac{x - 1}{x ^{2}})

- \infty

Solution steps

x \to 0 - lim (\frac{x - 1}{x ^{2}})

Divide by highest denominator power:

\frac{1}{x} - \frac{1}{x ^{2}}

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

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

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

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

f (t) = sin (t^{2})

\frac{d y}{d x} + (\frac{7}{x}) y = 2 x + 3

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

f (x) = \frac{x}{1 + x ^{2}}, 0.4, at x = 2

x \to 0 lim (1^{\frac{1}{x}})

What is the limit as x approaches 0-of (x-1)/(x^2) ?
The limit as x approaches 0-of (x-1)/(x^2) is -infinity