What is the limit as x approaches 1 of xln|x-1| ?

The limit as x approaches 1 of xln|x-1| is -infinity

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limit as x approaches 1 of xln|x-1|

x \to 1 lim (x ln ∣ x - 1 ∣)

- \infty

Solution steps

x \to 1 lim (x ln ∣ x - 1 ∣)

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 1 - lim (x ln ∣ x - 1 ∣) = - \infty

x \to 1 + lim (x ln ∣ x - 1 ∣) = - \infty

= - \infty

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

x \to - 1 lim (5 x)

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

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

x \to - 2 lim (3 x - \frac{6}{x})

What is the limit as x approaches 1 of xln|x-1| ?
The limit as x approaches 1 of xln|x-1| is -infinity