Home
Class 12
MATHS
Prove that the function f(x)={x/(|x|+2...

Prove that the function `f(x)={x/(|x|+2x^2),x!=0 and k ,x=0` remains discontinuous at `x=0`, regardless the choice of `k`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos
  • DEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|562 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f(x)={x/(|x|+2x^2),\ \ \ x!=0k ,\ \ \ x=0 remains discontinuous at x=0 , regardless the choice of k .

Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if x ne 0),(k, if x = 0):} remains discontinuous at x = 0 , regardings the choice iof k.

Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if x ne 0),(k, if x = 0):} remains discontinuous at x = 0 , regardings the choice iof k.

Prove that f(x)={((x-|x|)/x, x!=0),( 2 , x=0):} is discontinuous at x=0 .

Show that the function f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " x= 0):}, is discontinuous at x=0.

The function f(x)={sinx/x +cosx , x!=0 and f(x) =k at x=0 is continuous at x=0 then find the value of k

For what value of k is the function f(x)={(sin2x)/x ,\ \ \ x!=0k ,\ \ \ x=0 continuous at x=0 ?

If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , then the value of k is 0 (b) 1 (c) -1 (d) e

Find k if the function f(x)={(sin3x)/x ,x!=0;k/2,x=0 is continuous at x=0 . (a)3 (b) 6 (d) 9 (d) 12

The function f(x)={(sin3x)/x ,x!=0k/2,x=0 is continuous of x=0,t h e nk= 3 (b) 6 (d) 9 (d) 12

RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. The function f(x)={x^2a a,if1lt=x<sqrt(2),if0lt=1(2b^2-4b)/(x^2),ifsqr...

    Text Solution

    |

  2. Iff(x)={(x-4)/(|x-4|)+a,ifx<4 a+b,if x = 4 (x-4)/(|x-4|)+b,if x >4 is ...

    Text Solution

    |

  3. Prove that the function f(x)={x/(|x|+2x^2),x!=0 and k ,x=0 remains d...

    Text Solution

    |

  4. Show that f(x)={((sin3x)/(tan2x) ,, if x<0),(3/2 ,, if x=0),((log(1+3...

    Text Solution

    |

  5. Find all point of discountinuity of the function f(t) = (1)/(t^(2)...

    Text Solution

    |

  6. Given the function f(x)=1/(x+2). Find the points of discontinuity of t...

    Text Solution

    |

  7. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (...

    Text Solution

    |

  8. Let f(x)=(log(1+x/a)-log(1-x/b))/x ,x!=0. Find the value of f at x=0...

    Text Solution

    |

  9. Let f(x)=(tan(pi/4-x))/(cot2x),x!=pi/4 . The value which should be as...

    Text Solution

    |

  10. The function f(x)=(x^3+x^2-16 x+20)/(x-2) is not defined for x=2. In o...

    Text Solution

    |

  11. The value of b for which the function f(x)={5x-4,0xlt=1 , 4x^2+3b x...

    Text Solution

    |

  12. If f(x)=1/(1-x), then the set of points discontinuity of the function ...

    Text Solution

    |

  13. If the function f(x) defined by f(x)=(log(1+3x)-"log"(1-2x))/x , x!...

    Text Solution

    |

  14. Show that f(x)=5x-4 , 0< x < 1 f(x)=4x^3-3x , 1< x <2 continuous a...

    Text Solution

    |

  15. If f(x)={asinpi/2(x+1), ,xlt=0(tanx-sinx)/(x^3),x >0 is continuous...

    Text Solution

    |

  16. If f(x)=(1-sinx)/((pi-2x)^2),when x!=pi/2 and f(pi/2)=lambda, the ...

    Text Solution

    |

  17. The value of k which makes f(x)={sinx/x ,x!=0, and k , ...

    Text Solution

    |

  18. Show that the function f(x)=2x-|x| is continuous at x=0.

    Text Solution

    |

  19. If the function f(x)=(2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at e...

    Text Solution

    |

  20. Let f(x)={(x-4)/(|x-4|a+b)+a ,x<0 (x-4)/(|x-4|)+b ,x >0 Then, f(x) i...

    Text Solution

    |