CSIR NET Mathematics Solution June 2018 | Question 67 | Real Analysis | Function Bounded Variation

[@prabu3232]

Very clearly explain thank u sir🙏

[@amuthaganesang8353]

Bounded variation problems are defined on closed interval. How can you solve this problem?

[@roseline3085]

Thank you for your service of teaching

[@debamitachatterjee5566]

Hi, thanks for making such helpful video. One thing i want to tell you. The 2nd function also monotone on the given domain. But that was not bounded variation. So monotonicity does not enough for be a bdd variation. If we consider the function on closed domain then monotonicity is enough to be bdd variation. So you should write on clsd interval for 4th option. Thank you.

[@mathematics4311]

Sir sinx function is bounded variation on any open interval true or false

[@priyagp24]

f'(x) is minus infinity at x=1 and -1. How it will be greater than zero on [-1,0]

[@ahsanhafeez349]

You can't put -1 becoz it is open half interval at -1 ok Similarly if you put -0.9 than it multiplies with minus sign and makes it positive, thats why at (-1,0] it gives greater than 0.

[@irshadsirslectures4446]

@@ahsanhafeez349 as x--> 1 , f'(x) ----> infnty, that is derivative is not bounded