What is the limit as x approaches-infinity of (5+2x)/(sqrt(9+4x^2)) ?

The limit as x approaches-infinity of (5+2x)/(sqrt(9+4x^2)) is -1

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limit as x approaches-infinity of (5+2x)/(sqrt(9+4x^2))

x \to - \infty lim (\frac{5 + 2 x}{9 + 4 x ^{2}})

- 1

Solution steps

x \to - \infty lim (\frac{5 + 2 x}{9 + 4 x ^{2}})

Expand

\frac{5 + 2 x}{9 + 4 x ^{2}} : \frac{5}{9 + 4 x ^{2}} + \frac{2 x}{9 + 4 x ^{2}}

= x \to - \infty lim (\frac{5}{9 + 4 x ^{2}} + \frac{2 x}{9 + 4 x ^{2}})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to - \infty lim (\frac{5}{9 + 4 x ^{2}}) + x \to - \infty lim (\frac{2 x}{9 + 4 x ^{2}})

x \to - \infty lim (\frac{5}{9 + 4 x ^{2}}) = 0

x \to - \infty lim (\frac{2 x}{9 + 4 x ^{2}}) = - 1

= 0 - 1

Simplify

= - 1

\int \frac{x + 3}{4 - x ^{2}} d x

2 x + 1, at x = \frac{1}{4}

n = 1 \sum \infty e^{- n} n!

f (x) = 8^{x}

x \to 8 - lim (\frac{2}{x - 8})

What is the limit as x approaches-infinity of (5+2x)/(sqrt(9+4x^2)) ?
The limit as x approaches-infinity of (5+2x)/(sqrt(9+4x^2)) is -1