Home
Class 12
MATHS
Let f(x) be positive, continuous, and d...

Let `f(x)` be positive, continuous, and differentiable on the interval `(a , b)a n d lim_(x->a^+)f(x)=1,lim_(x->b^-)f(x)=3^(1/4)dot` If `f^(prime)(x)geqf^3(x)+1/(f(x)),` then the greatest value of `b-a` is (a)`pi/(48)` (b) `pi/(36)` (c)`pi/(24)` (d) `pi/(12)`

Promotional Banner

Similar Questions

Explore conceptually related problems

Suppose f(x)={(a+bx, x 1):} and if lim_(xto1) f(x)=f(1), what are the values of a and b?

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,where theta in (-pi,pi], then the value of theta is (a)+-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

Let f(x)=(k cos x)/(pi-2x) if x!=(pi)/(2) and f(x=(pi)/(2)) if x=(pi)/(2) then find the value of k if lim_(x rarr(pi)/(2))f(x)=f((pi)/(2))

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a)-1 (b). 1 ( c.) 0 (d).2

Let f(x)=(1-tan x)/(4x-pi),x!=(pi)/(4),x in[0,(pi)/(2)], If f(x) is continuous in [0,(pi)/(4)], then find the value of f((pi)/(4))

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

If f(x)=cos[pi^(2)]x+cos[-pi^(2)]x, where [x] stands for the greatest integer function,then (a) f((pi)/(2))=-1( b) f(pi)=1( c) f(-pi)=0 (d) f((pi)/(4))=1

If f(x) is differentiable and strictly increasing function,then the value of lim_(x rarr0)(f(x^(2))-f(x))/(f(x)-f(0)) is 1 (b) 0(c)-1 (d) 2