Home
Class 12
MATHS
If xgt0, then show that log(1+x)gt(x)/(1...

If `xgt0`, then show that `log(1+x)gt(x)/(1+x)`.

Text Solution

Verified by Experts

The correct Answer is:
`implies log(1+x)gt(x)/(1+x)," when "xgt0`
Promotional Banner

Topper's Solved these Questions

  • QUESTIONS PAPER -2019

    CHHAYA PUBLICATION|Exercise HS 2019 PART -B|10 Videos

  • QUESTIONS PAPER -2019

    CHHAYA PUBLICATION|Exercise WBJEE 2019|45 Videos

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT-4|4 Videos

  • RANDOM VARIABLE AND ITS DISTRIBUTION

    CHHAYA PUBLICATION|Exercise Assertion Reason Type|8 Videos

Similar Questions

Explore conceptually related problems

answer any three questions: 3.if x>0, then show that log(1+x) > x/(1+x).

If x gt 0 , show that, log (1+x) lt x

If x int_(0)^(x)sin(f(t))dx=(x+2)int_(0)^(1)tsin(f(t))dt , where xgt0 , then show that f'(x)cot f(x)+3/(1+x)=0

If x gt 0 , show that, x gt log (1+x) gt x-x^(2)/2 .

If x gt 0 , show that, x gt sin x

If x gt 0 , show that, x gt log (x^(2)+1)

If x gt 0 , show that, x^(2) gt (1+x) [log (1+x)]^(2)

If x gt 0 , show that, 1+x log (x+sqrt(x^(2)+1)) gt sqrt(1+x^(2))

If x gt 0 , prove that, x gt log (1+x) gt x/(1+x)

If 3f(x)-f(1/x)=log_(e)x^(4)(xgt0) , then prove that f(e^(x))=x .

CHHAYA PUBLICATION-QUESTIONS PAPER -2019-WBJEE 2019
  1. If xgt0, then show that log(1+x)gt(x)/(1+x).

    Text Solution

    |

  2. lim(xto0+)(x^n lnx),ngt0

    Text Solution

    |

  3. If intcosxlog(tan""(x)/(2))=sinxlog(tan""(x)/(2))+f(x) then f(x) is eq...

    Text Solution

    |

  4. y=intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx is a equation of a family of

    Text Solution

    |

  5. The value of integration int(-(pi)/(4))^((pi)/(4))(lambda|sinx|+(musin...

    Text Solution

    |

  6. The value of lim(xto0)(1)/(x)[inty^ae^(sin^2t)dt-int(x+y)^ae^(sin^2t)d...

    Text Solution

    |

  7. If int2^(2^x)*2^xdx=A*2^(2^x)+c, then A=

    Text Solution

    |

  8. The value of the integral int(-1)^(1){(x^(2015))/(x^2+cosx)}dx is equa...

    Text Solution

    |

  9. lim(ntooo)(3)/(n){1+sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt((n)/(n+9))+.....

    Text Solution

    |

  10. The general solution of the differential equation (1+e^((x)/(y)))dx+(1...

    Text Solution

    |

  11. General solution of (x+y)^2(dy)/(dx)=a^2,ane0 is

    Text Solution

    |

  12. Let P(4,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1. If t...

    Text Solution

    |

  13. If the radius of a spherical balloon increases by 0.1%, then its volum...

    Text Solution

    |

  14. Let A be a square matrix of order 3 whose all entries are 1 and let I3...

    Text Solution

    |

  15. If M is any square matrix of order 3 over R and if M' be the transpose...

    Text Solution

    |

  16. If A=({:(5,5x,x),(0,x,5x),(0,0,5):}) and |A^2|=25, then |x| is equal t...

    Text Solution

    |

  17. Let A and B be two square matrices of order 3 and AB=O3, wher O3 denot...

    Text Solution

    |

  18. Let: RtoR be defined by f(x)=x^2-(x^2)/(1+x^2) for all x inR. Then

    Text Solution

    |

  19. Let the relation p be defined on R as apb iff 1+abgt0. Then

    Text Solution

    |

  20. A problem in mathematics is given to 4 students whose chances of solvi...

    Text Solution

    |

  21. If X is a random variable such that sigma(X)=2.6," then "sigma(1-4X) i...

    Text Solution

    |