What is the limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4)) ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4))

x \to \infty lim (\frac{4 x ^{2} + 5 x}{10 + x ^{4}})

4

Solution steps

x \to \infty lim (\frac{4 x ^{2} + 5 x}{10 + x ^{4}})

Expand

\frac{4 x ^{2} + 5 x}{10 + x ^{4}} : \frac{4 x ^{2}}{10 + x ^{4}} + \frac{5 x}{10 + x ^{4}}

= x \to \infty lim (\frac{4 x ^{2}}{10 + x ^{4}} + \frac{5 x}{10 + x ^{4}})

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{4 x ^{2}}{10 + x ^{4}}) + x \to \infty lim (\frac{5 x}{10 + x ^{4}})

x \to \infty lim (\frac{4 x ^{2}}{10 + x ^{4}}) = 4

x \to \infty lim (\frac{5 x}{10 + x ^{4}}) = 0

= 4 + 0

Simplify

= 4

3 y^{^{''}} - 12 y = 0

x \to 0 + lim (\frac{1}{x ^{3} - 2 x ^{2}})

y = x^{4} + 5 x^{2} - x

\int cos (\frac{nπ x}{2}) d x

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

What is the limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4)) ?
The limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4)) is 4