What is the limit as y approaches-3 of sqrt((y^2-9)/(2y^2+7y+3)) ?

The limit as y approaches-3 of sqrt((y^2-9)/(2y^2+7y+3)) is sqrt(6/5)

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limit as y approaches-3 of sqrt((y^2-9)/(2y^2+7y+3))

y \to - 3 lim (\frac{y ^{2} - 9}{2 y ^{2} + 7 y + 3})

\frac{6}{5}

Decimal

1.09544 \dots

Solution steps

y \to - 3 lim (\frac{y ^{2} - 9}{2 y ^{2} + 7 y + 3})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= y \to - 3 lim (\frac{y ^{2} - 9}{2 y ^{2} + 7 y + 3})

Simplify

\frac{y ^{2} - 9}{2 y ^{2} + 7 y + 3} : \frac{y - 3}{2 y + 1}

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

Plug in the value

y = - 3

= \frac{- 3 - 3}{2 ( - 3 ) + 1}

Simplify

\frac{- 3 - 3}{2 ( - 3 ) + 1} : \frac{6}{5}

= \frac{6}{5}

16 y^{^{''}} - y = 0, y (- 7) = 1, y^{^{'}} (- 7) = - 1

\frac{d}{d x} (x^{\frac{5}{3}} - 5 x^{\frac{2}{3}})

\frac{d}{d x} (tan (x) + \frac{1}{x})

y = 8 x

x \to π - lim (csc (x))

What is the limit as y approaches-3 of sqrt((y^2-9)/(2y^2+7y+3)) ?
The limit as y approaches-3 of sqrt((y^2-9)/(2y^2+7y+3)) is sqrt(6/5)