Question

lim(x->0)[msinx/x]=8. [ ]is the greatest integer function.Find the value of m.?
Can anyone tell me which the value of m 8 or 9.

Answer 1

@sourwing

Answer 2

you can use L'Hopitals rule for this problem, do you know what it is?

Answer 3

Yes,But i am confused between 8 and 9.

Answer 4

okay since you know as x -> 0 you get a 0/0 so you apply L' Hopitals rule to it and get

\[\frac{ mcos(x) }{ 1 } = 8\]

so by apply L'Hopitals Rule, you can just subsitute x with 0
and you can solve for m

Answer 5

But the greates integer function doesnot matters??

Answer 6

sorry i didnt notice those brackets. In that case the [] means you always round down
so when you take the limit from the left and right direction you will get values close to 0 and the greatest integer function will round it down to 0

Answer 7

if you look at the graph of
8 sin x/x , you will find that when x->0\(^-\), the graph is just below 8, and hence the floor value makes it 7.
similarly, at x->0\(^+\) also.

and similarly, if you see graph of 9 sin x/x, at x->0, on both sides, the graph is just below 9, which makes the floor value and limit as 8.

Answer 8

Thanks@hartnn

Answer 9

welcome ^_^