What is the limit as x approaches 1 of (x^x-1)/(x*ln(x)) ?

The limit as x approaches 1 of (x^x-1)/(x*ln(x)) is 1

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limit as x approaches 1 of (x^x-1)/(x*ln(x))

x \to 1 lim (\frac{x ^{x} - 1}{x \cdot ln ( x )})

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

= \frac{1 ^{1} ( ln ( 1 ) + 1 )}{ln ( 1 ) + 1}

Simplify

= 1

x \to \infty lim (sin (2))

x \to 1 lim (x ln (sin (\frac{x}{2})))

x \to 3 lim (x^{2} - 6 x + 9)

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

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

What is the limit as x approaches 1 of (x^x-1)/(x*ln(x)) ?
The limit as x approaches 1 of (x^x-1)/(x*ln(x)) is 1