-1

In the following function $$f(x)= \begin{cases} \left(\frac{6}{5}\right)^{\frac{\tan 6x}{\tan 5x}},& \mbox{ if } 0<x<\frac{\pi}{2}\\ b+2,&\mbox{ if }x=\frac{\pi}{2}\\ \left(1+|\cos x|\right)^{\frac{a|\tan x|}{b}},&\mbox{ if }\frac{\pi}{2}<x<\pi \end{cases} $$ We have to determine the values of $a$ & $b$ , if $f$ is continuous at $x=1/2\pi$.

I am confused how to solve the limit at LHL of $x=1/2\pi$ . As in there the power is of form $0/0$ . Could we use L hopital in these type of problem .

Juniven Acapulco
  • 9,654
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
  • 1,769
  • Do you mean at $x=\frac12\pi$? – barak manos Dec 22 '16 at 17:02
  • 2
    I don't see $0/0$ anywhere in this problem. I recommend to edit the question, showing more of the details of your work on the problem--which limit you were working on, what fraction is going to $0/0,$ and so forth. And use MathJax so that we can correctly read the math you're writing: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – David K Dec 22 '16 at 17:09

1 Answers1

1

Hint for Lhs limit

put $$t=\frac{\pi}{2}-x$$

then $$f(x)=(\frac{6}{5})^{\frac{\tan( -6t) }{ \tan(\frac{\pi}{2}-5t )}}$$

which goes to $1$.

hamam_Abdallah
  • 62,951