6is it mod x +a or mod (x+a)
16 Answers
11if a is some integer then the value of a is 1(the lowest integer for which there is no solution...)
(i think its |x|+a)
6it sud be slightly above 2sinx
coz max value of 2sinx =2
so a will be from (2,∞)
bhaiya can dis be a solution??
no real root meaning graph of 2sinx will not cut mod x +a nytime
6@sandipan how did u make such a beautiful graph??/
it took a lot of pain for me to make d sinx graph in paint??
6ohh m sry sandipan ur right....
my graph is aweful ..so i got d right ans.......
11I used a software for plotting graphs...otherwise to draw the graphs of sin cos...becomes really painful in paint....
11I used a software for plotting graphs...otherwise to draw the graphs of sin cos...becomes really painful in paint....
in fact Kalyan u r rite...
a can range from 1 to infinity...
is rite bhaiya??
11Bhaiya i meant to say that the lowest integral value of a is 1.
becuase lowest integral value below 1 is zero...but at a=0 y=|x| cuts the graph of y=2sin x ....thus there would be some solution...
at a=1 y=|x|+1 does not cut the graph of y=2sin x so there's no solution...
11i got mixed up bhaiya ...... is it something because of this..???
LHS attains max at x = pi/2 ...maximum value = 2
so |(pi)/2| ≈ 1.7....
so minimum value of a is 1 so that R.H.S > L.H.S due to which no soln.
???
62no sandipan...
Think of it in one of the two ways..
a) Tangent
b) Maxima Minima!
Dont know if you are getting the clue!
11is it this Bhaiya??
y = 2 sin x
dy/dx = 2 cos x
now we now slope of y = |x| is tan 45o = 1 (considering only the part in the 1st quadrnt)
so 2 cos x = 1
x = (pi)/3
so y = √3
so we need the tangent at ((pi)/3 , √3)
so eqn of tangent comes out to be y = x + (√3 - (pi)/3)
now given y = x + a shud be above the tangent..for no solution..
so a > (√3 - (pi)/3) = 0.686
so least integral value of a is 1.