What is the limit as x approaches 3-of (x-3)^{-1} ?

The limit as x approaches 3-of (x-3)^{-1} is -infinity

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limit as x approaches 3-of (x-3)^{-1}

x \to 3 - lim ((x - 3)^{- 1})

- \infty

Solution steps

x \to 3 - lim ((x - 3)^{- 1})

Apply exponent rule:

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

= x \to 3 - lim (\frac{1}{x - 3})

For

x

approaching

3

from the left

, x < 3 \Rightarrow x - 3 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

\frac{\partial}{\partial y} (ln (10 x^{2} - 7 y^{2}))

f (x) = \frac{4 - 3 x - x ^{2}}{x ^{2} - 1}

\int 10 arcsin (x) d x

x \to - 2 lim ((x + 1) (x + 3))

What is the limit as x approaches 3-of (x-3)^{-1} ?
The limit as x approaches 3-of (x-3)^{-1} is -infinity