Home
Class 12
MATHS
For all x in (0, 1) :...

For all `x in (0, 1)` :

A

`e^(x) lt 1+x`

B

`log (1+x) lt x`

C

`sin x gt x`

D

`log_(e) x gt x`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise Multiple Choice Questions LEVEL-II|35 Videos
  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise Latest Questions from AIEEE/JEE Examinations|13 Videos
  • AREA UNDER CURVES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (Question from karnataka CET & COMED)|9 Videos

Similar Questions

Explore conceptually related problems

Let f be a real valued function defined on the interval (-1,1) such that e^(-x) f(x) = 2 + int_0^x sqrt(t^4 + 1) dt , for all x in (-1, 0) and let f^(-1) be the inverse function of f. Then (f^(-1))'(2) is equal to :

The set of values of a for which the inequality, x^2 + ax + a^2 + 6a < 0 is satisfied for all x in (1, 2) lies in the interval:

If |ax^2 + bx+c|<=1 for all x is [0, 1] ,then

The number of all the possible triplets (a_1,a_2,a_3) such that a_1+a_2cos(2x)+a_3sin^2(x)=0 for all x is (a) 0 (b) 1 (c) 3 (d) infinite

Let f be differentiable for all x. If f(1)= -2, f'(x) ge 2 for all x in [1, 6] , then :

The values of p and q for which the function : f(x) = {{:((sin (p + 1)x + sin x)/(x), x lt 0),(q,x=0),((sqrt(x + x^(2)) - sqrt(x))/(x^(3//2)),x gt 0):} is : continuous for all x in R, are :

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is

Let f be a function defined for all x in R . If f is differentiable and f(x^(3)) = x^(5) for all x in R (x ne 0) , then the value of f^(')(27) is

Let f(x) satisfy the requirements of Largrange's Mean Value Theorem in [0, 2]. If f(0) = 0 and |f'(x)| le (1)/(2) , for all x in [0, 2], then :

MODERN PUBLICATION-APPLICATION OF DERIVATIVES -Recent Competitive Questions (Questions from Karnataka CET & COMED)
  1. For all x in (0, 1) :

    Text Solution

    |

  2. P is the point of contact of the tangent from the orign to the c...

    Text Solution

    |

  3. For the curve 4x^(5)=5y^(4), the ratio of the cube of the sub-tangent ...

    Text Solution

    |

  4. The set of real values of x for which f(x)=(x)/(logx) is increasing is...

    Text Solution

    |

  5. A wire of lenggth 20 cm is bent in the form of a sector of a circle. T...

    Text Solution

    |

  6. If for the curve y=1+bx-x^(2) the tangent at (1, -2) is parallel to x-...

    Text Solution

    |

  7. The slopes of the tangent and normal at (0, 1) for the curve y=sinx+e^...

    Text Solution

    |

  8. A stone is thrown vertically upwards and the height x ft, reached by ...

    Text Solution

    |

  9. If sin^(-1) a is the acture angle between the curves x^(2) + y^(2) =4x...

    Text Solution

    |

  10. The maximum area of rectangle that can be inscribed in a circle of rad...

    Text Solution

    |

  11. A stone is dropped into a quiet lake and waves in circles at the speed...

    Text Solution

    |

  12. A gardener is digging a plot of land. As he gets tired, he works more ...

    Text Solution

    |

  13. If f(x)=x^(3) and g(x)=x^(3)-4x in -2lt x lt 2, then consider the stat...

    Text Solution

    |

  14. The tangent to the curve y=x^(3)+1 at(1, 2) makes an angle theta with ...

    Text Solution

    |

  15. The maximum value of ((1)/(x))^(2x^(2)) is :

    Text Solution

    |

  16. Let x be a number which exceeds its square by the greatest possible qu...

    Text Solution

    |

  17. The sub tangent at x=(pi)/(2) on the curve y=sin x is :

    Text Solution

    |

  18. A balloon which always remains spherical is being inflated by pump...

    Text Solution

    |

  19. The two curves x^(3) - 3xy^(2) + 2 = 0 and 3x^2y - y^(3) = 2

    Text Solution

    |

  20. If x is real, the minimum value of x^(2)-8x+17 is :

    Text Solution

    |

  21. The slant height of a cone is fixed at 7 cm. If the rate of increase ...

    Text Solution

    |