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

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

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

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

- \infty

Solution steps

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

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

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= 3 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to π lim (x - 3.1416)

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

x \to 0 + lim (csc (x) cot (x))

x \to - 4 + lim (\frac{x + 4}{∣ x + 4 ∣})

x \to \infty lim (2 - 3 x)

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