13is the ans .....exactly 1 in pie/6 to pie/3
but u ve not given it as an option..........:(
the equation x- cosx =0 has a.exactly one root in (0,pi/6 ) b.exactly one root in (pi/6,pi/3) c.exactly one root in (pi/3, pi/2) d. has infinite solution in (0, pi/2) i tried to draw the graphs of y= cosx and y=x on the same graph paper but couldn't judge !!help
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9 Answers
13
1i am really sorry guys and gals the second one is (pi/6,pi/3) and this is the correct answer too ... hello skygirl , i know it seems to be in this range only.........but how can we be sure about it ..what if there is a option of "none of these" ....how do we actually get it ??
1f(Î /6) < 0 and f(Î /3) > 0 ..... implies the point lies in d interval of (Î /6,Î /3).....
this is d only possible shortest method to solve such problems... formal methods do exist but they are a li'l bit cumbersome...
if u need logic, then go wid dis... if u need a complete mathematical solution, then let me know, i'll try to find one !! :)
1f'(x)=1+sinx>0 when x (pi/6,pi/3)
or its monotonic,
also dat f(pi/6)<0 and f(pi/3)>0,
=> ders exactly 1 root in the interval,
cheers!!