What is the limit as x approaches 0+of x^{-4} ?

The limit as x approaches 0+of x^{-4} is infinity

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limit as x approaches 0+of x^{-4}

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

\infty

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

For

x

approaching

0

from the right

, x > 0 \Rightarrow x^{4} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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

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

x \to \infty lim (- 12 x^{5})

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

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

What is the limit as x approaches 0+of x^{-4} ?
The limit as x approaches 0+of x^{-4} is infinity