Home
Class 12
MATHS
Let f(x)=(3)/(4)x+1,f^(n)(x) be defined ...

Let `f(x)=(3)/(4)x+1,f^(n)(x)` be defined as `f^(2)(x)=f(f(x)),` and for `n ge 2, f^(n+1)(x)=f(f^(n)(x))." If " lambda =underset (n to oo)(lim)f^(n)(x),` then show that λ is independant of x.

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

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

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Let f(x)=int_2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Then the value of g'(0)

f_(n)(x)=e^(f_(n-1)(x))" for all "n in N and f_(0)(x)=x," then "(d)/(dx){f_(n)(x)} is

If f (x)=underset(nrarroo)"lim"(1)/(1+x^(2n)) find f (x) for all real x .

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

If f(x)=(a-x^n)^(1/n)," where "a gt0 and n is a positive integer, show that f[f(x)]=x.

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot

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

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in R an...

    Text Solution

    |

  2. Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",", x ge 3):} and g(x)={(x-3"...

    Text Solution

    |

  3. Let f(x)=(3)/(4)x+1,f^(n)(x) be defined as f^(2)(x)=f(f(x)), and for n...

    Text Solution

    |

  4. If f:{1,2,3....}->{0,+-1,+-2...} is defined by f(n)={n/2, if n is ...

    Text Solution

    |

  5. If f: Rrarr[0,oo)is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), th...

    Text Solution

    |

  6. If p and q are positive integers, f is a function defined for positive...

    Text Solution

    |

  7. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  8. Show that any function can be expressed as the sum of an odd function ...

    Text Solution

    |

  9. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  10. Each question has four choices, a,b,c and d,out of which only one is ...

    Text Solution

    |

  11. Let f(x)=log2 log3log4log5(sin x+a^2). Find the set of values of a for...

    Text Solution

    |

  12. Let f(x)={x^2-4x+3, ,x<3; x-4,xgeq3 a n d g(x)={x-3,x<4; x^2...

    Text Solution

    |

  13. If fa n dg are two distinct linear functions defined on R such that th...

    Text Solution

    |

  14. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that ...

    Text Solution

    |

  15. Let f:XtoY be a function defined by f(x)=asin(x+pi/4)+bcosx+c. If f is...

    Text Solution

    |

  16. If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx ...

    Text Solution

    |

  17. Let R="{"x , y")": x , y in R ,x^2+y^2lt=25}andR^(prime)={(x , y): x ...

    Text Solution

    |

  18. A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c le...

    Text Solution

    |

  19. The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes...

    Text Solution

    |

  20. If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetric ab...

    Text Solution

    |