Home
Class 12
MATHS
f(x) = 1 + [cosx]x in 0 leq x leq pi/2 ...

`f(x) = 1 + [cosx]x` in `0 leq x leq pi/2` (where [.] denotes greatest integer function) then

A

it is continuous in `0ltxltπ/2`

B

it is differentiable in `0ltxltπ/2`

C

its maximum value is 2

D

it is not differentiable in `0ltxltπ/2`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

The number of integers in the range of function f(x)= [sinx] + [cosx] + [sinx + cosx] is (where [.] = denotes greatest integer function)

Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ [cos x],,, 0 le x le pi),( [sin x] -[cos x],,, pi lt x le 2pi):} where {.} denotes greatest integer function then. Number of points where f (x) is non-derivable :

The function f(x)=1+x(sinx)[cosx], 0ltxlepi//2 , where [.] denotes greatest integer function

The function f(x)=1+x(sinx)[cosx], 0ltxlepi//2 , where [.] denotes greatest integer function

Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(2)) where [] denotes the greatest integer function then f(x) is

Let f(x) = (sin (pi [ x - pi]))/(1+[x^2]) where [] denotes the greatest integer function then f(x) is

If f(x) =2 [x]+ cos x , then f: R ->R is: (where [ ] denotes greatest integer function)

If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

Discuss the continuity and differentiability for f(x) = [sin x] when x in [0, 2pi] , where [*] denotes the greatest integer function x.

Prove that f(x) = [tan x] + sqrt(tan x - [tan x]) . (where [.] denotes greatest integer function) is continuous in [0, (pi)/(2)) .

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. The tens digit of 1!+2!+3!++73 ! is : 1 (2) 2 (3) 3 (4) 4

    Text Solution

    |

  2. Find the derivative of f(tan x) w.r.t. g (sec x) at x=(pi)/(4), where ...

    Text Solution

    |

  3. f(x) = 1 + [cosx]x in 0 leq x leq pi/2 (where [.] denotes greatest in...

    Text Solution

    |

  4. If A=[2 5 7 9 0 1 9 7 0 0 -1 8 0 0 0 1] then the value of |a d j(a ...

    Text Solution

    |

  5. The number of real roots of the equation x^5+e^(8x)=0 is (1)0 (2) ...

    Text Solution

    |

  6. The total number of selection of letters "ned needs nineteen nets" is ...

    Text Solution

    |

  7. Find the value of sum(p=1)^n(sum(m=p)^n.^nCm.^m Cp)dot And hence, find...

    Text Solution

    |

  8. If f continuous and differentiable on [0,1] with f(0)= 0 and f(1)=1, t...

    Text Solution

    |

  9. The tangent at a point P on a curve meets x-axis in A. If area of t...

    Text Solution

    |

  10. The position vectors of points A, B, C are respectively hat i- hat j-...

    Text Solution

    |

  11. Solution of the differential equation y(a x y+e^x)dx-e^x dy=0 where y(...

    Text Solution

    |

  12. If the planes x-cy-bz=0, cx-y+az=0 and bx+ay-z=0 pass through a line, ...

    Text Solution

    |

  13. In a triangle OAC, if B is the mid point of side AC and vec O A= vec ...

    Text Solution

    |

  14. C is the complex numbers f:CrarrR is defined by f(z)=|z^(3)-z+2|. Find...

    Text Solution

    |

  15. Find the number of points where the function f(x) = max(|tanx|,cos|x|)...

    Text Solution

    |

  16. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

    Text Solution

    |

  17. Let there are three points A (0, 4/3), B(–1, 0) and C(1, 0) in x – y p...

    Text Solution

    |

  18. Let f(x) be an increasing function defined on (0,oo) . If f(2a^2+a+1)>...

    Text Solution

    |

  19. Let f:[-(5pi)/(12),-pi/3]vecR is a function f(x)=tan(x+(2pi)/3)-tan(x+...

    Text Solution

    |

  20. If f (x) be a differentiable function satisfying f (y) f ((x)/(y))=f (...

    Text Solution

    |