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

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

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

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

\frac{3}{2}

Decimal

1.5

Solution steps

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

Simplify

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

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

= \frac{\frac{3}{1}}{\frac{1}{1 ^{2}} + \frac{1}{1}}

Simplify

\frac{\frac{3}{1}}{\frac{1}{1 ^{2}} + \frac{1}{1}} : \frac{3}{2}

= \frac{3}{2}

\frac{d}{d x} (\frac{sin ( 6 x )}{e ^{3 x}})

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 5)

\frac{3}{( s - 3 ) ( s + 1 )}

\frac{\partial}{\partial x} (r^{2} s t + r s^{2} t + rs t^{2})

\frac{1}{3} \frac{d x}{d t} - 2 e^{- t} = - x

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