What is the limit as x approaches 0 of (sqrt(x+2)-2)/(sqrt(2x+5)-3) ?

The limit as x approaches 0 of (sqrt(x+2)-2)/(sqrt(2x+5)-3) is ((2-sqrt(2))(3+sqrt(5)))/4

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limit as x approaches 0 of (sqrt(x+2)-2)/(sqrt(2x+5)-3)

x \to 0 lim (\frac{x + 2 - 2}{2 x + 5 - 3})

\frac{( 2 - 2 ) ( 3 + 5 )}{4}

Decimal Notation

0.76680 \dots

Solution steps

x \to 0 lim (\frac{x + 2 - 2}{2 x + 5 - 3})

Plug in the value

x = 0

= \frac{0 + 2 - 2}{2 \cdot 0 + 5 - 3}

Simplify

\frac{0 + 2 - 2}{2 \cdot 0 + 5 - 3} : \frac{( 2 - 2 ) ( 3 + 5 )}{4}

= \frac{( 2 - 2 ) ( 3 + 5 )}{4}

\int cos (x) \cdot sin^{3} (x) d x

\frac{d}{d x} (\frac{1}{x ^{2} cos ( x )})

y^{^{'}} = 135 y x^{4}

f (x) = (5 x^{3} + 2) (3 x^{3} + 2)

n = 1 \sum \infty \frac{n - 1}{9 n - 1}

What is the limit as x approaches 0 of (sqrt(x+2)-2)/(sqrt(2x+5)-3) ?
The limit as x approaches 0 of (sqrt(x+2)-2)/(sqrt(2x+5)-3) is ((2-sqrt(2))(3+sqrt(5)))/4