Home
Class 12
MATHS
If f(x)=lim(n->oo)[2x+4x^3+6x^5++2n x...

If `f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)]` `(0ltxlt1)` then `int f(x)dx` is equal to:

A

`-sqrt(1-x^(2))`

B

`(1)/(sqrt(1-x^(2)))`

C

`(1)/((x^(2)-1))`

D

`(1)/(1-x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise OBJECTIVE|84 Videos

  • TIPS

    FIITJEE|Exercise ASSERTION REASONING|8 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

If (x)=lim_(n rarr oo)[2x+4x^(3)+6x^(5)++2nx^(2n-1)]f(x)=lim_(n rarr oo)[2x+4x ^(3)+6x^(5)++2nx^(2n-1)](0

If f(x)=lim_(n->oo) {2x+4x^3+...+2n x^(2n-1)}, 0 < x< 1 and int f(x) dx = F(x) and F(1/sqrt(2)) = 2, then (i) F(0)=1, (ii) F(1/2)=4/3, (iii) F(0)=-1, (iv) F(-1/2)=4/3

If f(x)=lim_(n rarr oo)n^(2)(x^((1)/(n))-x^((1)/(n)+1)),x>0 then int xf(x)dx is

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

If f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1),x in R, the the the points where f(x) is not continuous are

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

Let f(x)=lim_(n to oo) sinx/(1+(2 sin x)^(2n)) then f is discontinuous at

int_(0)^(a)f(2a-x)dx=m and int_(0)^(a)f(x)dx=n then int_(0)^(2a)f(x)dx is equal to

Let f(x)=lim_(n rarr oo)(cos x)/((1+tan^(-1)x)^(n)), then int_(0)^(oo)f(x)dx=

FIITJEE-TIPS-ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)
  1. If f(x) ={x} + sin ax (where { } denotes the fractional part function)...

    Text Solution

    |

  2. Which of the following is differentiable in the interval (1, 2)?

    Text Solution

    |

  3. If f(x)=lim(n-&gt;oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(...

    Text Solution

    |

  4. The integer n for which the lim(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x...

    Text Solution

    |

  5. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

    Text Solution

    |

  6. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  7. If f is twice differentiable such that f"(x)=-f(x) f'(x)=g(x),h'(x)=...

    Text Solution

    |

  8. lim(x->0) (tan^2[x])/([x]^2), where [] represents greatest integer fun...

    Text Solution

    |

  9. lim(xrarr1^(+))(log(sqrt2)sqrt2x)^(1/({x})) where [ ] represents great...

    Text Solution

    |

  10. The value of lim(xto(pi)/4)(4sqrt(2)-(cosx+sinx)^(5))/(1-sin2x) is

    Text Solution

    |

  11. lim(xrarrpi)([sinx]+x) is

    Text Solution

    |

  12. The slope of the tangent of the curve y=int0^x (dx)/(1+x^3) at the poi...

    Text Solution

    |

  13. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

    Text Solution

    |

  14. The difference between the greatest and the least values of the functi...

    Text Solution

    |

  15. Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increas...

    Text Solution

    |

  16. If f(1)(x)=2x, f(2)x(=3 sin x-x cos x, for x in (0, (pi)/(2))

    Text Solution

    |

  17. Let f(x)=x^3+kx^2+5x+4sin^2x be an increasing function on x in R. Th...

    Text Solution

    |

  18. Let g'(x)gt 0 and f'(x) lt 0 AA x in R, then

    Text Solution

    |

  19. If x1 and x2 are abscissae of two points on the curve f(x) = x - x^2 i...

    Text Solution

    |

  20. f(x)={ax^2+bx+c, |x| > 1 x+1, |x| <= 1. If f(x) is continuous for all ...

    Text Solution

    |