What is the limit as x approaches 0-of [xln|x|-x] ?

The limit as x approaches 0-of [xln|x|-x] is 0

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limit as x approaches 0-of [xln|x|-x]

x \to 0 - lim ([x ln ∣ x ∣ - x])

0

Solution steps

x \to 0 - lim (x ln ∣ x ∣ - x)

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim (x ln (- x) - x)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 - lim (x ln (- x)) - x \to 0 - lim (x)

x \to 0 - lim (x ln (- x)) = 0

x \to 0 - lim (x) = 0

= 0 - 0

Simplify

= 0

\frac{\partial}{\partial y} (x^{ey})

y = tan^{2} (7 x)

\frac{d}{d x} (x 800 - x)

\int \frac{( x - 9 )}{( x + 5 ) ( x - 2 )} d x

\int \frac{x ^{3} - 1}{x ^{2} + 3 x + 2} d x

What is the limit as x approaches 0-of [xln|x|-x] ?
The limit as x approaches 0-of [xln|x|-x] is 0