Home
Class 12
MATHS
If f(x)={{:((sin[x])/([x])","" ""for "[...

If `f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):}`where `[x]` denotes the greatest integer less than or equal to x. Then find `underset(xto0)limf(x).`

Text Solution

Verified by Experts

The correct Answer is:
Does not exists
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL -1|134 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL 2|103 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

If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).

Let [x] denote the greatest integer less than or equal to x . Then, int_(0)^(1.5)[x]dx=?

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

Let [x] denotes the greatest integer less than or equal to x and f(x)=[tan^(2)x] . Then

Examine Lim_(xto 2) [ x] , where [ x] denotes the greatest integar less than or equal to x.

lim_(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer less than or equal to x, is

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

let [x] denote the greatest integer less than or equal to x. Then lim_(xto0) (tan(pisin^2x)+(abs.x-sin(x[x]))^2)/x^2

If [x] denotes the greatest integer less than or equal to x , then find the value of the integral int_0^2x^2[x]dxdot

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):...

    Text Solution

    |

  2. Let g: R -> R be a differentiable function with g(0) = 0,,g'(1)!=0.Let...

    Text Solution

    |

  3. Let f(x)=sin((pi)/(6)sin((pi)/(2)sinx)) " for all "x in R and g(x)=(pi...

    Text Solution

    |

  4. Let f:R to R and h:R to R be differentiable functions such that f(x)=x...

    Text Solution

    |

  5. Let a , b in R and f:R to R be defined by f(x) =a cos (|x^(3)-x|)+...

    Text Solution

    |

  6. Let f:[-1/2,2] rarr R and g:[-1/2,2] rarr R be functions defined by f(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |