What is the limit as x approaches infinity of (e^x+sin(x))/(e^x+cos(x)) ?

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 (e^x+sin(x))/(e^x+cos(x))

x \to \infty lim (\frac{e ^{x} + sin ( x )}{e ^{x} + cos ( x )})

1

Solution steps

x \to \infty lim (\frac{e ^{x} + sin ( x )}{e ^{x} + cos ( x )})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{e ^{x} + cos ( x )}{e ^{x} - sin ( x )})

= x \to \infty lim (\frac{e ^{x} + cos ( x )}{e ^{x} - sin ( x )})

Apply the Squeeze Theorem:

1

= 1

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

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

x \to 2 lim (3 x^{2} + 8 x - 1)

x \to 0 lim ((x sin (\frac{1}{x}))^{2})

x \to \frac{- π}{2} lim (sec (x))

What is the limit as x approaches infinity of (e^x+sin(x))/(e^x+cos(x)) ?
The limit as x approaches infinity of (e^x+sin(x))/(e^x+cos(x)) is 1