What is the limit as x approaches infinity of 13x(e^{1/x})-13x ?

The limit as x approaches infinity of 13x(e^{1/x})-13x is 13

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 13x(e^{1/x})-13x

x \to \infty lim (13 x (e^{\frac{1}{x}}) - 13 x)

13

Solution steps

x \to \infty lim (13 x e^{\frac{1}{x}} - 13 x)

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

13 x e^{\frac{1}{x}} - 13 x = x (13 e^{\frac{1}{x}} - 13)

= x \to \infty lim (x (13 e^{\frac{1}{x}} - 13))

Rewrite for L'Hopital

= x \to \infty lim (\frac{- 13 + 13 e ^{\frac{1}{x}}}{\frac{1}{x}})

Apply L'Hopital's Rule

: x \to \infty lim \frac{- \frac{13 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

= x \to \infty lim \frac{- \frac{13 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

Simplify

\frac{- \frac{13 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : 13 e^{\frac{1}{x}}

= x \to \infty lim (13 e^{\frac{1}{x}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 13 \cdot x \to \infty lim (e^{\frac{1}{x}})

Apply the Limit Chain Rule:

1

= 13 \cdot 1

Simplify

= 13

y^{^{'}} = 8 - \frac{y}{200} 4, y (0) = 50

x \to \frac{π}{4} lim (sin (2 x))

\int_{- 1}^{2} \frac{x ^{2}}{3} d x

\frac{d}{d x} (\frac{4 sin ( x )}{5 cos ( y )})

f (x) = 2 x^{2} - 5 x + 2, at x = a

What is the limit as x approaches infinity of 13x(e^{1/x})-13x ?
The limit as x approaches infinity of 13x(e^{1/x})-13x is 13