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

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

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 (x^2)/(sqrt(x^4+2))

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

1

Solution steps

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

Divide by highest denominator power:

\frac{1}{1 + \frac{2}{x ^{4}}}

= x \to \infty lim \frac{1}{1 + \frac{2}{x ^{4}}}

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to \infty lim (1) = 1

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

= \frac{1}{1}

Simplify

= 1

\frac{d}{d x} (\frac{( 1 - x ^{2} )}{( x ^{2} + 1 ) ^{2}})

2 t x d x + (t^{2} - x^{2}) d t = 0

y = \frac{9}{x}

\int_{0}^{2} \frac{1}{2} d x

5 x - 4 x

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