continuity-doubt

[Xiang]

let f(x)=tan(pi/4-x)/cot2x, x not equal to pi/4.
The value which should be assigned to f(x) at x-pi/4 so that it is continuous everywhere is- ?

I really dont know how to go about doing it. Please help.

thank you

[cx]

wat r the options!

e. Briefly,
a function f has a removable discontinuity at x = a if lim
x→a
f(x) exists and either f(a) is
undefined or lim
x→a
f(x) = f(a).

here i think we have this discontinuity so it cant be made continuous should be d ans!

[Amit Goyal]

f(x) at x = pi/4 should be 1/2, i.e. f(pi/4) = 1/2, for f to be continuous everywhere. Working is attached:
evaluating_limit.png

[Xiang]

oh ok!

we could get answer without using the l'hospitol rule but it is a little cumbersome.

Thank you Amit sir

[cx]

sorry!

i mis read the problem, basically when one gets limit equal to 0//0, one differentiates and then find the limit!

but tell me if using la hospital repeatedly we get 0/0 then will tat be called a irremovable discontinuity?

tks