What is the limit as x approaches 3 of (x-1)/(x^2+1) ?

The limit as x approaches 3 of (x-1)/(x^2+1) is 1/5

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limit as x approaches 3 of (x-1)/(x^2+1)

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

\frac{1}{5}

Decimal Notation

0.2

Solution steps

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

Plug in the value

x = 3

= \frac{3 - 1}{3 ^{2} + 1}

Simplify

\frac{3 - 1}{3 ^{2} + 1} : \frac{1}{5}

= \frac{1}{5}

x \to 0 lim (\frac{4}{sin ( x )})

x \to 0 + lim (\frac{ln ( x )}{x - 1})

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

x \to \infty lim (\frac{x ^{2} - 9}{x \cdot ( x ^{2} + 1 )})

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

What is the limit as x approaches 3 of (x-1)/(x^2+1) ?
The limit as x approaches 3 of (x-1)/(x^2+1) is 1/5