Home
Class 12
MATHS
f(x)=lim(mrarroo){lim(nrarroo)cos^(2m)n!...

`f(x)=lim_(mrarroo){lim_(nrarroo)cos^(2m)n!pix}` then

A

2 or 1 according as x is rational or irrational

B

1 or 2 according as x is rational or irrational

C

1 for all x

D

2 or 1 for all x

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

Similar Questions

Explore conceptually related problems

If f(x)=lim_(m->oo) lim_(n->oo)cos^(2m) n!pix then the range of f(x) is

Let f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1, if x is rational and 0, if x is irrational

Let alpha = Lt_(mrarroo) Lt_(nrarroo) cos^(2m) |__n pix , where x is rational, beta= Lt_(mrarroo) Lt_(nrarroo) cos^(2m) |__n pix, where \'x\' is irrational, then the area of the triangle having vertices (alpha, beta), (-2, 1) and (2, 1) is (A) 2 (B) 4 (C) 1 (D) none of these

Let f(x)=(log_e(x^2+e^x))/(log_e(x^4+e^2x)) . If lim_(xrarr oo) f(x)=l and lim_(xrarr-oo)f(x)=m , then

If (cos x)/(sin ax) is periodic function, then lim_(mrarroo)(1+cos^(2m)n!pia) is equal to

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

The value of I=lim_(nrarroo)Sigma_(r=1)^(n)(r)/(n^(2)+n+r) is equal to

Let f(x)= lim_(n->oo)(sinx)^(2n)

Let the given function is differentiable at x = 1. f(x)={{:(lim_(nrarroo) (ax(x-1)(cot.(pix)/(4))^(n)+(px^(2)+2))/((cot,(pix)/(4))^(n)+1)",",x in(0,1)uu(1,2)),(0",",x=1):} Then the value of |a+p| is

Evaluate the limit: ("lim")_(nrarroo)cos(pisqrt(n^2+n)) when n is an integer

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
  1. lim(n->oo)(1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+....n/(n^2+n))

    Text Solution

    |

  2. Evaluate underset(xto-1^(+))lim(sqrt(pi)-sqrt(cos^(-1)x))/(sqrt(1+x)).

    Text Solution

    |

  3. f(x)=lim(mrarroo){lim(nrarroo)cos^(2m)n!pix} then

    Text Solution

    |

  4. lim(xrarr1)(sin(e^(x-1)-1))/(log x) is equal to

    Text Solution

    |

  5. The value of lim(xrarroo) ((x-1)/(x+1))^(x), is

    Text Solution

    |

  6. Let f(x) = 1 /(sqrt( 18 - x^2) The value of Lt(x -> 3) (f(x)-f(3)) / ...

    Text Solution

    |

  7. If f(x)=2/(x-3),g(x)=(x-3)/(x+4),a n dh(x)=-(2(2x+1))/(x^2+x-12),t h e...

    Text Solution

    |

  8. The value of lim(xrarr0) (a^x-b^x)/(x) ,is

    Text Solution

    |

  9. The value of lim(xrarr0) (e^x-(x+x))/(x^2),is

    Text Solution

    |

  10. lim(xrarr1) (1+cos pix)cot^2pi x is equal to

    Text Solution

    |

  11. The value of lim(xto0) (int(0)^(x)tdt)/(xtan (x+pi)) is equal to

    Text Solution

    |

  12. The value of lim(xrarroo) ((x^2+6)/(x^2-6))^(x) is given by

    Text Solution

    |

  13. If [x] denotes the greatest integer less than or equal to x,then the v...

    Text Solution

    |

  14. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0. Then ...

    Text Solution

    |

  15. If f(x)={(xsin,((1)/(x)),xne0),(0,,x=0):} Then, lim(xrarr0) f(x)

    Text Solution

    |

  16. lim(xto-pi)(|x+pi|)/(sin x) is

    Text Solution

    |

  17. If lim(x->oo) (sqrt(x^2-x+1)-ax-b)=0 then the value of a and b are giv...

    Text Solution

    |

  18. lim(xto1) (sum(r=1)^(n)x^(r)-n)/(x-1) is equal to

    Text Solution

    |

  19. lim(x->pi/4)(2sqrt(2)-(cosx+sinx)^3)/(1-sin2x)=

    Text Solution

    |

  20. The value of lim(n->oo)(1.sum(r=1)^n(r)+2.sum(r=1)^(n-1)(r)+3sum(r=1)^...

    Text Solution

    |