Home
Class 11
MATHS
Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n...

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``

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

A function is defined as, f(x)={(0, where x is rational),(1, where x is irrational)}: . Then f(x) is

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then f has

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the range of x.

The area of the triangle having vertices (-2,1), (2,1) and (lim_(mtoinftyntoinfty)cos^(2m)(n!pix) , x is rational lim_(mtoinftyntoinfty)cos^(2m)(n!pix) , where x is irrational) is

If f(x) = lim_(nrarr infty)(sinx)^(2n) where n in l^+ then f(x) is

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

Let for all xgt0,f(x)=lim_(nto oo)n(x^((1)/(n))-1) , then

f(x)=(lim)_(n->oo)(sin(pix/2))^(2n) for x >0,x!=1 ,and f(1)=0. Discuss the continuity at x=1.

Let f(x) = ((1 - x(1+ |1-x | )) /(|1-x|)) cos(1/(1-x)) for x!=1 then prove that lim_(xto1^(-)) f(x)=0

Let f(x)={lim_(n->oo)(a x(x-1)(cot((pix)/4))^n+(p x^2+2))/((cot((pix)/4))^n+1) ,x in (0,1) uu (1,2) and 0 ,x=1 If f(x) is differentiable for all x in (0, 2) then (a^2 +p^2) equals

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. lim(x->0)(e^(5x) - 1)/(3x)

    Text Solution

    |

  2. lim(x->(pi/2)) (1-sinx)tanx =

    Text Solution

    |

  3. The value of lim(x->3)((x^3+27)(log)e(x-2))/(x^2-9) is a. 9 b. 18 c....

    Text Solution

    |

  4. If (lim)(xvec0)(e^(a x)-e^x-x)/(x^2)=b (finite), then a=2,b=0 b. a=0,b...

    Text Solution

    |

  5. If underset(xrarr0)(lim)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is...

    Text Solution

    |

  6. underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the...

    Text Solution

    |

  7. The value of lim(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

    Text Solution

    |

  8. lim(x->0) (sin x /x)

    Text Solution

    |

  9. If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the gr...

    Text Solution

    |

  10. If A=underset(xrarr0)(lim)(sin^(-1)(sinx))/(cos^(-1)(cosx))and B=under...

    Text Solution

    |

  11. Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then...

    Text Solution

    |

  12. lim(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional par...

    Text Solution

    |

  13. Let f(x)=(lim)(xvecoo)(tan^(-1)(tanx))/(1+((log)e x)^n),x!=(2n+1)pi/2 ...

    Text Solution

    |

  14. Assume that underset(thetararr-1)(lim)f(theta) exists and (theta^(2)+t...

    Text Solution

    |

  15. lim(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

    Text Solution

    |

  16. Let f: RvecR be such that f(a)=1,f^(prime)(a)=2. Then (lim)(xvec0)((...

    Text Solution

    |

  17. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

    Text Solution

    |

  18. If a >0,b >0 then (lim)(n->oo)((a-1+b^(1/n))/a)^n= b^(1//a) b. a^...

    Text Solution

    |

  19. (lim)(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 ...

    Text Solution

    |

  20. If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xv...

    Text Solution

    |