What is the limit as x approaches infinity of (x+3)^{1/(x^2)} ?

The limit as x approaches infinity of (x+3)^{1/(x^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+3)^{1/(x^2)}

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

1

Solution steps

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

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{x ^{2}} l n (x + 3)})

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (\frac{e ^{8 x} - e ^{- 4 x}}{ln ( 1 + x )})

n \to \infty lim (\frac{2 n + 1}{1 - 3 n})

x \to 0 lim (\frac{ln ( 10 x + 1 )}{x})

x \to 0 lim (1 - \frac{tan ( 3 x )}{x})

x \to 4 + lim (10 - 2 x)

What is the limit as x approaches infinity of (x+3)^{1/(x^2)} ?
The limit as x approaches infinity of (x+3)^{1/(x^2)} is 1