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

The limit as x approaches 1 of (x^2+1)/(x+6) is 2/7

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

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

\frac{2}{7}

Decimal Notation

0.28571 \dots

Solution steps

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

Plug in the value

x = 1

= \frac{1 ^{2} + 1}{1 + 6}

Simplify

= \frac{2}{7}

x \to 8 lim (\frac{x ^{2} - 8 x}{x ^{2} - 7 x - 8})

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

x \to 5 lim (3 x - 5)

x \to 40 lim (15)

x \to 5 - lim (- \frac{3}{x + 5})

What is the limit as x approaches 1 of (x^2+1)/(x+6) ?
The limit as x approaches 1 of (x^2+1)/(x+6) is 2/7