What is the limit as x approaches 0-of (4-x)/x ?

The limit as x approaches 0-of (4-x)/x is -infinity

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limit as x approaches 0-of (4-x)/x

x \to 0 - lim (\frac{4 - x}{x})

- \infty

Solution steps

x \to 0 - lim (\frac{4 - x}{x})

Divide by highest denominator power:

\frac{4}{x} - 1

= x \to 0 - lim (\frac{4}{x} - 1)

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{4}{x}) - x \to 0 - lim (1)

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

x \to 0 - lim (1) = 1

= - \infty - 1

Apply Infinity Property:

- \infty - c = - \infty

= - \infty

\int \frac{x ^{2} + 1}{x ( x - 1 ) ^{3}} d x

\int sin (3 x) sin (2 x) d x

x^{2} - 8 x + 16

\int_{2}^{\infty} \frac{1}{x ^{3}} d x

y^{^{'}} - 2 y = 3 e^{t}

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