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

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

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

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

- \infty

Solution steps

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

Divide by highest denominator power:

1 - \frac{2}{x}

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

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

x \to 0 + lim (1) = 1

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

= 1 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

\frac{d}{d x} (cos (2 x) + sin (2 x) + \frac{1}{5} e^{x})

\frac{s}{( s - 3 ) ( s - 4 ) ( s - 12 )}

\frac{\partial}{\partial x} (2 x^{\frac{3}{2}})

y = - x^{2} + 6 x, y = x^{2} - 2 x

\frac{3}{5 x ^{4}}

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