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

The limit as x approaches infinity of (sqrt(5x^4+2x))/(x^2) is square root of 5

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

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

5

Decimal

2.23606 \dots

Solution steps

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

Divide by highest denominator power:

5 + \frac{2}{x ^{3}}

= x \to \infty lim (5 + \frac{2}{x ^{3}})

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

With the exception of indeterminate form

= x \to \infty lim (5 + \frac{2}{x ^{3}})

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 (5) + x \to \infty lim (\frac{2}{x ^{3}})

x \to \infty lim (5) = 5

x \to \infty lim (\frac{2}{x ^{3}}) = 0

= 5 + 0

Simplify

= 5

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