Originally Posted by

**Vamz** $\displaystyle

\displaystyle \lim_{x\to \pi^+} \left(4x-4\pi \right)\tan\!\left(\frac{x}{2}\right)

$

$\displaystyle

\displaystyle let f(x)=(4x-4\pi) ; g(x)=\tan(\frac{x}{2})

$

so, therefore

$\displaystyle

\displaystyle Lim( f(x)* g(x) ) = Lim f(x) * Lim g(x)

$

for g(x)

$\displaystyle

\displaystyle U=\frac{x}{2}

$

$\displaystyle

\displaystyle U*\frac{\tan U}{U} = U * 1 = U

$

So, the limit for g(x) is $\displaystyle \displaystyle\frac{\pi}{2}$

Now, for dealing with f(x)

$\displaystyle

\displaystyle (4x-4\pi) =0

$

no matter how I move these variables around, f(x) always ends up zero, sending my entire limit to zero - which is incorrect! What am I missing here?

Thanks!