Home
Class 12
MATHS
Let f(x)=(1-x(1+|1-x|))/(|1-x|)cos((1)/(...

Let` f(x)=(1-x(1+|1-x|))/(|1-x|)cos((1)/(1-x))" for "x ne1.` then

A

`lim_(xto1^(-)f(x)` does not exist

B

`lim_(xto1^(+)) f(x)` does not exist

C

`lim_(xto1^(-)f(x)=0`

D

`lim_(xto1^(+)f(x)=0`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos
  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = ((1 - x(1+ |1-x | )) /(|1-x|)) cos(1/(1-x)) for x!=1

Let f(x) = (x(2^(x)-1))/( 1- cos x) for x ne 0 what choice of f(0) , if any, will make f (x) continuous at x = 0 ?

Let f(x)=(1)/(1-x)."Then (fo(fof)) (x)"

If f(x) = (1)/(1 -x) x ne 1 and g(x) = (x-1)/(x) , x ne0 , then the value of g[f(x)] is :

Let f(x)= {{:((x)/(1+|x|)",", |x| ge1), ((x)/(1-|x|)",", |x| lt 1):}, then domain of f'(x) is:

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)) . Then,

Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)) . Then,

If f(x)={{:(,(x-a)^(n)cos ((1)/(x-a)), x ne a),(,0,x=a):} then at x=a, f(x) is

Let f(x) = sin^(-1)|sin x| + cos^(-1)( cos x) . Which of the following statement(s) is / are TRUE ?

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Let f:[-1/2,2] rarr R and g:[-1/2,2] rarr R be functions defined by f(...

    Text Solution

    |

  2. Let [x] be the greatest integer less than or equal to x . Then ,...

    Text Solution

    |

  3. Let f(x)=(1-x(1+|1-x|))/(|1-x|)cos((1)/(1-x))" for "x ne1. then

    Text Solution

    |

  4. Let f be two differentiable function satisfying f(1)=1,f(2)=4, f(3)=9,...

    Text Solution

    |

  5. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

    Text Solution

    |

  6. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)...

    Text Solution

    |

  7. underset(xrarr(pi)/(4))(lim)(int(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/...

    Text Solution

    |

  8. (d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

    Text Solution

    |

  9. Let g(x) = log f(x), where f(x) is a twice differentiable positive fun...

    Text Solution

    |

  10. Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2 m and n integers, m ne0...

    Text Solution

    |

  11. If underset(xto0)lim[1+xln(1+b^(2))]^(1//x)=2bsin^(2)theta,bgt0," and ...

    Text Solution

    |

  12. Let f(x) = {{:(x^(2)|"cos"(pi)/(x)|",",x ne 0","x in R),(0",",x = 0):}...

    Text Solution

    |

  13. If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  14. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

    Text Solution

    |

  15. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  16. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |

  17. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

    Text Solution

    |

  18. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  19. Let f : R rarr R be a function such that f(x+y) = f(x) + f(y), AA x, y...

    Text Solution

    |

  20. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

    Text Solution

    |