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

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

If f(x)=sin^(-1)x then prove that lim_(x->1/2)f(3x-4x^3)=pi-3lim_(x->1/2)sin^(-1)x

If f(x) is a differentiable function for all x gt 0 and lim_(y to x)(y^(2)f(x)-x^(2)f(y))/(y-x)=2 , then the value of f'(x) is -

Let ("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

If int_a^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is ___

If the equation x^3+b x^2+c x+1=0,(b (a) -pi (b) -pi/2 (c) pi/2 (d) pi

If f(x)=cos[pi^2]x+cos[-pi^2]x then the value of f(pi/4)+f(pi/2) is

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

Let f(x)=e^(cos^-1sin(x+pi/3)) , then

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. The function f and g are positive and continuous. If f is increasing a...

    Text Solution

    |

  2. A Function f(x) satisfies the relation f(x)=e^x+int0^1e^xf(t)dtdot T...

    Text Solution

    |

  3. Let f(x) be positive, continuous, and differentiable on the interval ...

    Text Solution

    |

  4. Letf: (0,oo)->R andF(x^3)=int0^ (x^3)f(t)dt, if F(x^3)=x^3(x^2+x+1).Th...

    Text Solution

    |

  5. Ifg(x)=int0^x2|t|dt,then (a)g(x)=x|x| (b)g(x) is monotonic (c) g(x...

    Text Solution

    |

  6. Prove that the value of the integral, int(0)^(2a)(f(x))/(f(x)+f(2a-x)...

    Text Solution

    |

  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  8. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  9. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

    Text Solution

    |

  10. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

    Text Solution

    |

  11. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  12. (lim)(n to oo)n/(2^n)int0^2x^n dx equals

    Text Solution

    |

  13. Let f:[0,oo) to R be a continuous strictly increasing function, such t...

    Text Solution

    |

  14. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

    Text Solution

    |

  15. L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int(1/4)^(3/4)f(f(x...

    Text Solution

    |

  16. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

    Text Solution

    |

  17. Consider the polynomial f(x)=a x^2+b x+c dot If f(0)=0,f(2)=2, then th...

    Text Solution

    |

  18. Find the points at which the function f given by f(x)=x^3-3x has local...

    Text Solution

    |

  19. STATEMENT 1: If f(x) is continuous on [a , b] , then there exists a po...

    Text Solution

    |

  20. Each question contains statements given in two columns which have to b...

    Text Solution

    |