What is the limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25)) ?

The limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25)) is sqrt(13/10)

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limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25))

x \to - 5 lim (\frac{2 x ^{2} + 7 x - 15}{x ^{2} - 25})

\frac{13}{10}

Decimal

1.14017 \dots

Solution steps

x \to - 5 lim (\frac{2 x ^{2} + 7 x - 15}{x ^{2} - 25})

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

With the exception of indeterminate form

= x \to - 5 lim (\frac{2 x ^{2} + 7 x - 15}{x ^{2} - 25})

Simplify

\frac{2 x ^{2} + 7 x - 15}{x ^{2} - 25} : \frac{2 x - 3}{x - 5}

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

Plug in the value

x = - 5

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

Simplify

\frac{2 ( - 5 ) - 3}{- 5 - 5} : \frac{13}{10}

= \frac{13}{10}

What is the limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25)) ?
The limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25)) is sqrt(13/10)