What is the limit as x approaches 4 of (x^2-6)/(x+2) ?

The limit as x approaches 4 of (x^2-6)/(x+2) is 5/3

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limit as x approaches 4 of (x^2-6)/(x+2)

x \to 4 lim (\frac{x ^{2} - 6}{x + 2})

\frac{5}{3}

Decimal Notation

1.66666 \dots

Solution steps

x \to 4 lim (\frac{x ^{2} - 6}{x + 2})

Plug in the value

x = 4

= \frac{4 ^{2} - 6}{4 + 2}

Simplify

\frac{4 ^{2} - 6}{4 + 2} : \frac{5}{3}

= \frac{5}{3}

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

x \to 31 lim (31 - x)

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

x \to 39 lim (- x^{2} + 2 x + 1)

t \to 0 lim (\frac{ln ( 2 t + 1 )}{t})

What is the limit as x approaches 4 of (x^2-6)/(x+2) ?
The limit as x approaches 4 of (x^2-6)/(x+2) is 5/3