Question

f(x)
kcosx/pi-2x, if x=/= pi/2

3, if x = pi/2

Function f is continuous at x = pi/2

:( I can't do this type of continuity problem :( @rational

Answer 1

Hi rational :) I'm brushing up everything today :)

Answer 2

The reason I got stuck in this one is when it is not equal to pi/2, what should I substitute x as?

Answer 3

heyy its no different from previous problems :

LHL = RHL = f(pi/2)

Answer 4

What do I substitute x as? when it is not equal to pi/2?

Answer 5

find the limit as x->pi/2

Answer 6

but shouldn't you not use pi/2? its given in that right? unfortunately, this is one of the problems they asked in the exam last time.. I'm sure this exact type will come back this time

Answer 7

you're given `f(pi/2) = 3`
and everywhere else the function is given by `f(x) = kcosx/pi-2x`

for the function to be continuous at x=pi/2, the limit must equal the function value

Answer 8

so your supposed to plug in pi/2 regardless?

Answer 9

for the function to be continuous at \(x=\pi/2\), we must have
\[\lim\limits_{x\to \pi/2}~f(x) = f(\pi/2)\]

Answer 10

so if we write kcos(pi/2) directly, it will give a 0 since cos(pi/2) = 0 and the whole thing will be zero..

Answer 11

oh we're taking a little less than pi/2

Answer 12

whats exactly the expression ? can you use latex/parenthesis..