What is the limit as x approaches 2+of (e^{-x})/(2-x) ?

The limit as x approaches 2+of (e^{-x})/(2-x) is -infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 2+of (e^{-x})/(2-x)

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

- \infty

Solution steps

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

Simplify

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

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

For

x

approaching

2

from the right

, x > 2 \Rightarrow e^{x} (2 - x) < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

\int 2 x (x^{2} + 4)^{7} d x

\int_{0}^{2} - x^{3} d x

\int (3 x^{3} - 2 x^{2}) d x

3 x^{4} + x^{3} - 21 x^{2}

y = x (25.5)

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