What is the limit as x approaches 3 of 4/(x^2+2x+3) ?

The limit as x approaches 3 of 4/(x^2+2x+3) is 2/9

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limit as x approaches 3 of 4/(x^2+2x+3)

x \to 3 lim (\frac{4}{x ^{2} + 2 x + 3})

\frac{2}{9}

Decimal

0.22222 \dots

Solution steps

x \to 3 lim (\frac{4}{x ^{2} + 2 x + 3})

Plug in the value

x = 3

= \frac{4}{3 ^{2} + 2 \cdot 3 + 3}

Simplify

\frac{4}{3 ^{2} + 2 \cdot 3 + 3} : \frac{2}{9}

= \frac{2}{9}

What is the limit as x approaches 3 of 4/(x^2+2x+3) ?
The limit as x approaches 3 of 4/(x^2+2x+3) is 2/9