Home
Class 12
MATHS
A function is definded as f(x) = lim...

A function is definded as
`f(x) = lim_( n to oo) {{:(cos^(2n)x, if xlt 0),(root(n)(1+x^(n)), if 0 le x le 1),((1)/(1+x^(n)),if gt1):}`
which of the following does not hold good ?

A

a. continuous at `x=0` but discontinuous at `x=1`

B

b. continuous at `x=1` but discontinuous at `x=0`

C

c. discontinuous at both `x=1` and `x=0`

D

d. continuous at both `x=1` and `x=0`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
NA
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise Math|105 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

  • TEST SERIES

    RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

Similar Questions

Explore conceptually related problems

A function is defined as f(x)=lim_(x->oo)[cos^(2n) x , if x 1 which of the following does not hold good?

If phi(x)=lim_(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the following is correct

If f (x) = lim _( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of the following is/are true?

Let f(x)=lim_(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which of the following alternative(s) is/ are correct?

The equivalent definition of the function f(x)=lim_(n to oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)), x gt 0 , is

If f(x)=lim_(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal to

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

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

The function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(|x|)-1) .

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is:

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS
  1. Let P,Q,R and S be the feet of the perpendiculars drawn from point (1,...

    Text Solution

    |

  2. Let [.] denote G.I.F. and tge0 and S={(x,y):(x-T)^(2)+y^(2)leT^(2) whe...

    Text Solution

    |

  3. A function is definded as f(x) = lim( n to oo) {{:(cos^(2n)x, if ...

    Text Solution

    |

  4. If [.] denotes the greatest integer function and x,yepsilonR,"n" epsil...

    Text Solution

    |

  5. The number of solutions to |e^(|x|)-3|=K is

    Text Solution

    |

  6. Let f(x)={(x+1, -1lexle0),(-x,0ltxle1):} then

    Text Solution

    |

  7. If the angles subtended by two chords of a circle at the centre are ...

    Text Solution

    |

  8. Consider the function f(x)={{:(xsin(pi)/(x),"for"xgt0),(0,"for"x=0):} ...

    Text Solution

    |

  9. Which of the following is True?

    Text Solution

    |

  10. lim(xrarrc)f(x) does not exist for wher [.] represent greatest integ...

    Text Solution

    |

  11. f(x)is defined for xge0 & has a continuous derivative. It satisfies f(...

    Text Solution

    |

  12. Let A*B=A^(T)B^(-1) where A^(T) represents transpose of matrix A and B...

    Text Solution

    |

  13. Let A*B=A^(T)B^(-1) where A^(T) represents transpose of matrix A and B...

    Text Solution

    |

  14. A curve is represented parametrically by the equations x=e^(1)cost and...

    Text Solution

    |

  15. A curve is represented parametrically by the equations x=e^(1)cost and...

    Text Solution

    |

  16. Find the locus of the point of intersection of the perpendicular ta...

    Text Solution

    |

  17. If the points (2-x, 2, 2), (2, 2-y, 2) and (2, 2, 2-z) are coplanar th...

    Text Solution

    |

  18. cot^(-1)(-1/2)+cot^(-1)(-1/3) is equal to

    Text Solution

    |

  19. If the focus of a parabola is (3,3) and its directrix is 3x-4y=2 then ...

    Text Solution

    |

  20. If a(1),a(2),a(3),…a(n+1) are in arithmetic progression, then sum(k=0)...

    Text Solution

    |