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

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 (1+1/(2x+1))^{sqrt(x^{2-3)}}

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int_{0}^{1} (x^{2} - 3 x + 6) d x

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

y^{^{'''}} + y^{^{''}} = 3 e^{x} + 4 x^{2}

\frac{d y}{d t} - 2 t y = 9 t^{2} e^{t^{2}}

\frac{d y}{d x} = y sin (x), y (0) = 1

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