Home
Class 12
MATHS
Prove the following inequalities 1+co...

Prove the following inequalities `1+cotx\ lt=cotx/2\ AA\ x in (0,pi)`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

Prove that following inequalities sinxlt=xlt=tanx\ AA\ in [0,pi/2]

Prove the following inequalities : tan x gt x + x^(3)//3 "if " (0 lt x lt pi//2)

027 Solve the following inequalities @) are cotx-5 arc cotx +6>0 (ii) arc sinx> arc cosx (iii) tan (arc sinx)>1

Solve the following inequality: arc cot^(2)x-5 arc cotx+6gt0

Evaluate the following integrals: int((1-cotx)/(1+cotx))dx

Evaluate the following integral: int_0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ )+sqrt(tanx))dx

Evaluate the following integral: int_0^(pi//2)1/(1+cotx)dx

Prove the inequalities tan x gt x + x^(3) //3 " at" 0 lt x lt pi//2

Prove the inequalities 1 +1/2 x - (x^(2))/8 lt sqrt(1+x) lt 1 +1/2 x at 0 lt x lt oo

Evaluate the following limits: lim_(xrarr0)(cosec x-cotx)

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Find the value of a , if the equation x-sinx=a has a unique r...

    Text Solution

    |

  2. Find the intervals in which the given function increases or decreas...

    Text Solution

    |

  3. Prove the following inequalities 1+cotx\ lt=cotx/2\ AA\ x in (0,pi)

    Text Solution

    |

  4. Leg f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  5. Find the values of x where f(x)=sin(lnx)-cos(lnx) in strictly increasi...

    Text Solution

    |

  6. Prove that sin^2theta<thetasin(sintheta)for0<theta<pi/2dot

    Text Solution

    |

  7. Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x...

    Text Solution

    |

  8. f(x)=(x-2)|x-3| is monotonically increasing in (a)(-oo,5/2)uu(3,oo)...

    Text Solution

    |

  9. A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2)a n df(x) ...

    Text Solution

    |

  10. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

    Text Solution

    |

  11. The intervals of increase of f(x) defined by f(x)=int(-1)^x(t^2+...

    Text Solution

    |

  12. If mean value theorem holds good for the function f(x)=(x-1)/x on ...

    Text Solution

    |

  13. Let f(x)a n dg(x) be two continuous functions defined from RvecR , suc...

    Text Solution

    |

  14. Find the critical points of the function f(x)=2/3sqrt(x^3)-x/2+int1^x(...

    Text Solution

    |

  15. Let f(x)=x+\ sqrt(x)\ "o n"\ [1,4]dot The mean value theorem say...

    Text Solution

    |

  16. Consider f(x)=|1-x|\ \ 1\ lt=xlt=2\ a n d\ \ g(x)=f(x)+bsinpi/2\ ...

    Text Solution

    |

  17. If f is a continuous function on [0,1], differentiable in (0, 1) such ...

    Text Solution

    |

  18. If the function f(x)=2x^2 + 3x + 5 satisfies LMVT at x = 2 on the clo...

    Text Solution

    |

  19. Consider the function f(x)=8x^2-7x+5 on the interval [-6,6]dot Find th...

    Text Solution

    |

  20. Range of the function f(x)=(ln x)/(sqrt(x)) is (a)(-oo,\ e) (b) (-o...

    Text Solution

    |