What is the limit as x approaches 1+of 3/(ln(x))-2/(x-1) ?

The limit as x approaches 1+of 3/(ln(x))-2/(x-1) is infinity

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limit as x approaches 1+of 3/(ln(x))-2/(x-1)

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

\infty

Solution steps

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

Simplify

\frac{3}{ln ( x )} - \frac{2}{x - 1} : \frac{3 ( x - 1 ) - 2 ln ( x )}{ln ( x ) ( x - 1 )}

= x \to 1 + lim (\frac{3 ( x - 1 ) - 2 ln ( x )}{ln ( x ) ( x - 1 )})

Apply L'Hopital's Rule

: x \to 1 + lim (\frac{3 - \frac{2}{x}}{\frac{x - 1}{x} + ln ( x )})

= x \to 1 + lim (\frac{3 - \frac{2}{x}}{\frac{x - 1}{x} + ln ( x )})

Simplify

\frac{3 - \frac{2}{x}}{\frac{x - 1}{x} + ln ( x )} : \frac{3 x - 2}{x - 1 + x ln ( x )}

= x \to 1 + lim (\frac{3 x - 2}{x - 1 + x ln ( x )})

\frac{3 x - 2}{x - 1 + x ln ( x )} = (3 x - 2) \frac{1}{x - 1 + x ln ( x )}

= x \to 1 + lim ((3 x - 2) \frac{1}{x - 1 + x ln ( x )})

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

With the exception of indeterminate form

= x \to 1 + lim (3 x - 2) \cdot x \to 1 + lim (\frac{1}{x - 1 + x ln ( x )})

x \to 1 + lim (3 x - 2) = 1

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

y = \frac{4}{x}, (5, \frac{4}{5})

(ln (7 x))^{2}

\frac{\partial}{\partial x} (2^{- x})

\int \frac{8}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

\int_{- 2}^{1} x^{3} d x

What is the limit as x approaches 1+of 3/(ln(x))-2/(x-1) ?
The limit as x approaches 1+of 3/(ln(x))-2/(x-1) is infinity