Home
Class 12
MATHS
Let f(x)=[(sinx)/x]+[(2sin2x)/x]+.....+[...

Let `f(x)=[(sinx)/x]+[(2sin2x)/x]+.....+[(10sin10 x)/x]` (where [.] is the greatest integer function) Then the value of `("lim")_(xvec0)f(x)` equals (a) 55 (b) 164 (c) 165 (d) 375

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BOARD PAPER SOLUTIONS

    RESONANCE DPP|Exercise All Questions|70 Videos
  • DETERMINANTS

    RESONANCE DPP|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

If f(x)=[sin^(2) x] ([.] denotes the greatest integer function), then

lim_(x->0) ([(-5sinx)/x]+[(6sinx)/x] .(where [-] denotes greatest integer function) is equal to

Let f(x)=["sinx"/x], x ne 0 , where [.] denotes the greatest integer function then lim_(xto0)f(x)

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

If f(x)=cos|x|+[|(sin 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

Let f(x)=(x(sinx+tanx))/([(x+pi)/(pi)]-1//2) (where (.] denotes the greatest integer function) then find f"(0) .

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

If f(x)={x+(1)/(2),x =0 then [(lim)_(x rarr0)f(x)]= (where [.] denotes the greatest integer function)

RESONANCE DPP-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. underset(x to0)(lim)((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " th...

    Text Solution

    |

  2. Which of the following is true? pi/3>tan^(-1)pi/3 (b) pi/3<tan^(-1)pi...

    Text Solution

    |

  3. Let f(x)=[(sinx)/x]+[(2sin2x)/x]+.....+[(10sin10 x)/x] (where [.] is t...

    Text Solution

    |

  4. The sum of the series x/(1)+(2x^2)/(2)+(3x^3)/(3)+ is x e^x b. -x e...

    Text Solution

    |

  5. If a x^2+2h x y+b y^2=0, then (dy)/(dx) is equal to y/x (b) x/y (c) ...

    Text Solution

    |

  6. If f(x)=(log)x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e ...

    Text Solution

    |

  7. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

    Text Solution

    |

  8. Let g is the inverse function of fa n df^(prime)(x)=(x^(10))/((1+x^2))...

    Text Solution

    |

  9. If x=(1+t)/(t^3),y=3/(2t^2)+2/t ,t h e nx((dy)/(dx))^3-(dy)/(dx) is eq...

    Text Solution

    |

  10. If u=f(x),v=g(x), then the value of D^*(udotv) is (D^*u)v+(D^*v)u b. u...

    Text Solution

    |

  11. Let f(x)={((x-4)/(|x-4|)+a ,x<4),(a+b ,x=4),((x-4)/(|x-4|)+b ,x >4):} ...

    Text Solution

    |

  12. If f(x)=x^3+bx^2+cx+d and 0 < b^2 < c, then in (-oo,oo), (a) f(x) is...

    Text Solution

    |

  13. The point(s) of minimum of function, f(x)=4x^3-x|x-2|,x in [0,3] is x=...

    Text Solution

    |

  14. Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive func...

    Text Solution

    |

  15. Let f:(-1,1)vecR be a differentiable function with f(0)=-1 and f^(prim...

    Text Solution

    |

  16. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

    Text Solution

    |

  17. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

    Text Solution

    |

  18. If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h...

    Text Solution

    |

  19. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

    Text Solution

    |

  20. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)),w h e r eprod(i=1)^k ai st...

    Text Solution

    |