What is the limit as x approaches 5-of (x-5)*ln(5-x) ?

The limit as x approaches 5-of (x-5)*ln(5-x) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 5-of (x-5)*ln(5-x)

x \to 5 - lim ((x - 5) \cdot ln (5 - x))

0

Solution steps

x \to 5 - lim ((x - 5) ln (5 - x))

Rewrite for L'Hopital

= x \to 5 - lim (\frac{ln ( 5 - x )}{\frac{1}{- 5 + x}})

Apply L'Hopital's Rule

= x \to 5 - lim (\frac{- \frac{1}{5 - x}}{- \frac{1}{( - 5 + x ) ^{2}}})

Simplify

\frac{- \frac{1}{5 - x}}{- \frac{1}{( - 5 + x ) ^{2}}} : - x + 5

= x \to 5 - lim (- x + 5)

Plug in the value

x = 5

= - 5 + 5

Simplify

= 0

z \to 1 lim (\frac{x + y - 1}{z - 1})

x \to 2 lim (\frac{∣ x + 2 ∣}{x + 2})

x \to 4 lim (\frac{- 1}{x - 4})

n \to \infty lim (\frac{( sin ( n ) )}{n})

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

What is the limit as x approaches 5-of (x-5)*ln(5-x) ?
The limit as x approaches 5-of (x-5)*ln(5-x) is 0