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

The limit as v approaches 3 of (sqrt(v+1)-2)/(v-3) is 1/4

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limit as v approaches 3 of (sqrt(v+1)-2)/(v-3)

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Rationalize numerator

\frac{v + 1 - 2}{v - 3} : \frac{1}{v + 1 + 2}

= v \to 3 lim (\frac{1}{v + 1 + 2})

Plug in the value

v = 3

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

Simplify

\frac{1}{3 + 1 + 2} : \frac{1}{4}

= \frac{1}{4}

x \to 3 lim (\frac{x - 2}{x ^{2} - 9})

\int \frac{1}{x ^{2} + 4 x + 5} d x

f (x) = \frac{9}{x - 3}, at x = 2

y = e^{5}

\frac{d}{d x} (x^{\frac{3}{4}} - 3 x^{\frac{1}{4}})

What is the limit as v approaches 3 of (sqrt(v+1)-2)/(v-3) ?
The limit as v approaches 3 of (sqrt(v+1)-2)/(v-3) is 1/4