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Popular >

limit as x approaches 2 of (sqrt(x^2+6x)-2x)/(sqrt(x)-\sqrt{2)}

Solution

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

Solution

- \frac{3}{2}

+1

Decimal

- 2.12132 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 2 lim (\frac{\frac{x + 3}{x ^{2} + 6 x} - 2}{\frac{1}{2 x}})

= x \to 2 lim (\frac{\frac{x + 3}{x ^{2} + 6 x} - 2}{\frac{1}{2 x}})

Plug in the value

x = 2

= \frac{\frac{2 + 3}{2 ^{2} + 6 \cdot 2} - 2}{\frac{1}{2 2}}

Simplify

\frac{\frac{2 + 3}{2 ^{2} + 6 \cdot 2} - 2}{\frac{1}{2 2}} : - \frac{3}{2}

= - \frac{3}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the limit as x approaches 2 of (sqrt(x^2+6x)-2x)/(sqrt(x)-\sqrt{2)} ?
The limit as x approaches 2 of (sqrt(x^2+6x)-2x)/(sqrt(x)-\sqrt{2)} is -3/(sqrt(2))