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

For all `x in (0,1)`

A

` e^x lt 1 + x `

B

` log_e (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

  • FUNCTIONS

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (MATCHING ENTRIES )|4 Videos

  • FUNCTIONS

    ML KHANNA|Exercise ASSERTION / REASON|1 Videos

  • FUNCTIONS

    ML KHANNA|Exercise PROBLEM SET (3) |71 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    ML KHANNA|Exercise Problem Set (2) (Self Assessment Test)|8 Videos

  • HEIGHTS AND DISTANCES

    ML KHANNA|Exercise Problem Set (3) FILL IN THE BLANKS|9 Videos

Similar Questions

Explore conceptually related problems

Let f:(0,1) in (0,1) be a differenttiable function such that f(x)ne 0 for all x in (0,1) and f((1)/(2))=(sqrt(3))/(2) . Suppose for all x, lim_(x to x)(int_(0)^(1) sqrt(1(f(s))^(2))dxint_(0)^(x) sqrt(1(f(s))^(2))ds)/(f(t)-f(x))=f(x) Then, the value of f((1)/(4)) belongs to

Let f:(-1,1)rarrR be a differentiable function satisfying (f'(x))^4=16(f(x))^2 for all x in (-1,1) , f(0)=0. The number of such functions is

For all x epsilon(0,1)

Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=x for all x in R (b) x for all x in R-{1} (c) x for all x in R-{0,\ 1} (d) none of these

Let f:R-{0,1}rarr R be a function satisfying the relation f(x)+f((x-1)/(x))=x for all x in R-{0,1} . Based on this answer the following questions. f(-1) is equal to

Let f:(0,oo)rarr R be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in(0,oo) and f(1)=1, then

Let f:[0,1] rarr R be such that f(xy)=f(x).f(y), for all x,y in [0,1] and f(0) ne 0. If y=y(x) satisfies the differential equation, dy/dx=f(x) with y(0)=1, then y(1/4)+y(3/4) is equql to (A) 5 (B) 3 (C) 2 (D) 4

The set of all possible real values of a such that the inequality (x-(a-1))(x-(a^(2)-1))<0 holds for all x in(-1,3) is (0,1) b.(oo,-1] c.(-oo,-1) d.(1,oo)

A function g defined for all positive real numbers,satisfies g'(x^(2))=x^(3) for all x>0 and g(1)=1 compute g(4)

ML KHANNA-FUNCTIONS-PROBLEM SET (4)
  1. On which of the following intervals is the function f(x)=2x^2 - log |...

    Text Solution

    |

  2. y=[ x(x - 3)^2 ] increases for all values of x lying in the ...

    Text Solution

    |

  3. Let f(x)=inte^x (x - 1)(x-2) dx. Then f decreases in the interval

    Text Solution

    |

  4. Let f (x) = x^3 + ax^2 + bx + 5 sin^2 x be an increasing function on t...

    Text Solution

    |

  5. If f(x) =( lamda^2-1)/( lamda^2 +1) x^3 - 3x +5 is a decreasing f...

    Text Solution

    |

  6. Let f (x) = x^3 +6x^2 + px + 2. If the largest possible interval in w...

    Text Solution

    |

  7. If x^(2)/(f(4a))+y^(2)/(f(a^(2)-5)) represents an ellipse with major a...

    Text Solution

    |

  8. The function f (x) = loge (x^3 + sqrt(x^6 +1)) is of the following t...

    Text Solution

    |

  9. The function f(x) = cos (pi / x) is decreasing in the interval

    Text Solution

    |

  10. The function f (x) = sin^4 x+cos^4 x increases if

    Text Solution

    |

  11. Let f (x) = {{:( x^(3) - x^(2) + 10 x- 5 , "," , x le 1), ( -2x + log ...

    Text Solution

    |

  12. The set of all x for which log (1 + x) le x is

    Text Solution

    |

  13. For all x in (0,1)

    Text Solution

    |

  14. f(x)=(x)/(sinx ) and g(x)=(x)/(tanx) , where 0 lt x le 1 then in the...

    Text Solution

    |

  15. A function is matched below against an interval where it is supposed t...

    Text Solution

    |

  16. The function f(x) = ( log ( pi +x))/( log ( e +x)) is a decreasing fu...

    Text Solution

    |

  17. The function y=(x)/(x^2 - 6x -16 ) is a decreasing function in R-{-2,...

    Text Solution

    |

  18. The function y=sin^(-1) (1+x) increases in -2 lt x lt 0. Is it true?

    Text Solution

    |

  19. The larger of log (1 + x) and ( tan^(-1) x)/(1 +x) when x>0 is .........

    Text Solution

    |

  20. Find the interval of monotonicity of y= (1-x +x^(2))/(1 + x + x^(2))

    Text Solution

    |