What is the limit as h approaches 0-of (sqrt(6)-sqrt(5h^2+11h+6))/h ?

The limit as h approaches 0-of (sqrt(6)-sqrt(5h^2+11h+6))/h is -(11)/(2sqrt(6))

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limit as h approaches 0-of (sqrt(6)-sqrt(5h^2+11h+6))/h

h \to 0 - lim (\frac{6 - 5 h ^{2} + 11 h + 6}{h})

- \frac{11}{2 6}

Decimal

- 2.24536 \dots

Solution steps

h \to 0 - lim (\frac{6 - 5 h ^{2} + 11 h + 6}{h})

Multiply by the conjugate of

6 - 5 h^{2} + 11 h + 6 : \frac{- 5 h ^{2} - 11 h}{6 + 5 h ^{2} + 11 h + 6}

= h \to 0 - lim \frac{\frac{- 5 h ^{2} - 11 h}{6 + 5 h ^{2} + 11 h + 6}}{h}

Simplify

\frac{\frac{- 5 h ^{2} - 11 h}{6 + 5 h ^{2} + 11 h + 6}}{h} : - \frac{5 h + 11}{5 h ^{2} + 11 h + 6 + 6}

= h \to 0 - lim (- \frac{5 h + 11}{5 h ^{2} + 11 h + 6 + 6})

Plug in the value

h = 0

= - \frac{5 \cdot 0 + 11}{5 \cdot 0 ^{2} + 11 \cdot 0 + 6 + 6}

Simplify

- \frac{5 \cdot 0 + 11}{5 \cdot 0 ^{2} + 11 \cdot 0 + 6 + 6} : - \frac{11}{2 6}

= - \frac{11}{2 6}

What is the limit as h approaches 0-of (sqrt(6)-sqrt(5h^2+11h+6))/h ?
The limit as h approaches 0-of (sqrt(6)-sqrt(5h^2+11h+6))/h is -(11)/(2sqrt(6))