What is the limit as x approaches 2-of (x-2)ln(2-x) ?

The limit as x approaches 2-of (x-2)ln(2-x) is 0

Popular >

limit as x approaches 2-of (x-2)ln(2-x)

x \to 2 - lim ((x - 2) ln (2 - x))

0

Solution steps

x \to 2 - lim ((x - 2) ln (2 - x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Simplify

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

= x \to 2 - lim (- x + 2)

Plug in the value

x = 2

= - 2 + 2

Simplify

= 0

x \to \frac{1}{2} lim (x^{2} tan (π x))

x \to - \infty lim (2 \cdot (x))

x \to 0 lim (\frac{1}{3 x ^{\frac{2}{3}}})

x \to π lim (\frac{ln ( cos ( 2 x ) )}{( x - π ) ^{2}})

x \to 4 lim (x^{2} - 4 x + 3)

What is the limit as x approaches 2-of (x-2)ln(2-x) ?
The limit as x approaches 2-of (x-2)ln(2-x) is 0