What is the limit as x approaches 2-of 1/(x^2-5x+6) ?

The limit as x approaches 2-of 1/(x^2-5x+6) is infinity

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limit as x approaches 2-of 1/(x^2-5x+6)

x \to 2 - lim (\frac{1}{x ^{2} - 5 x + 6})

\infty

Solution steps

x \to 2 - lim (\frac{1}{x ^{2} - 5 x + 6})

For

x

approaching

2

from the left

, x < 2 \Rightarrow x^{2} - 5 x + 6 > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 0 + lim (f_{(x)} (x) (x))

x \to 0 lim (\frac{x ^{3} + 8 x}{3 x})

x \to 5 - lim (\frac{1}{( 5 - x ) ^{2}})

x \to 5 lim (\frac{x ^{3} - 8}{x - 2})

x \to 0 lim (\frac{5}{ln ( x ^{2} )})

What is the limit as x approaches 2-of 1/(x^2-5x+6) ?
The limit as x approaches 2-of 1/(x^2-5x+6) is infinity