What is the limit as x approaches 0-of (x^4-1)/(x^4) ?

The limit as x approaches 0-of (x^4-1)/(x^4) is -infinity

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limit as x approaches 0-of (x^4-1)/(x^4)

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

- \infty

Solution steps

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

Divide by highest denominator power:

1 - \frac{1}{x ^{4}}

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

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{1}{x ^{4}})

x \to 0 - lim (1) = 1

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

= 1 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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

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

x \to \infty lim (- x^{2} e^{x})

x \to 2 lim (\frac{1 - 4 x}{x + 3})

h \to 0 lim (\frac{ln ( 2 e + h ) - ln ( 2 e )}{h})

What is the limit as x approaches 0-of (x^4-1)/(x^4) ?
The limit as x approaches 0-of (x^4-1)/(x^4) is -infinity