Home
Class 12
MATHS
If ("lim")(xvec0)(x^n-sinx^n)/(x-sin^n x...

If `("lim")_(xvec0)(x^n-sinx^n)/(x-sin^n x)` is non-zero finite, then `n` must be equal to 4 (b) 1 (c) 2 (d) 3

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos

  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

If lim_(x to 0) (x^n-sin^n x)/(x-sin^n x) is nonzero and finite , then n in equal to

If lim_(x rarr0)(x^(n)*sin^(n)x)/(x^(n)-sin^(n)x) is non-zero finite,then n must be equal to 4(b)1(c)2(d)3

lim_(x rarr0)(x+sin x-x cos x-tan x)/(x^(n)) exists and is non-zero finite value then the value of n is: (a) 3 (b) 4 (c) 5 (d) 6

(2) lim_(n rarr0) (n!sin x)/(n)

lim_(x->0) (sin(nx)((a-n) nx-tan x))/ x2., when n is a non-zero positive integer, then a is equal to

("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))], where[dot] denotes the greatest integer function, is equal to 0 (b) 1 (c) -1 (d) does not exist

lim_(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero positive integer, then a is equal to

If lim_(x to 0) ({(a-n)nx - tan x} sin nx)/x^(2) = 0 , where n is non-zero real number, then a is equal to

If (lim)_(xvec0)(x^3)/(sqrt(a+x)(b x-sinx))=1,a >0t h e na+b is equal to a. 36 b. 37 c. 38 d. 40

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. ("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in ...

    Text Solution

    |

  2. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

    Text Solution

    |

  3. If ("lim")(xvec0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n m...

    Text Solution

    |

  4. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

    Text Solution

    |

  5. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  6. ABC is an isosceles triangle described in a circle of radius r.If AB=...

    Text Solution

    |

  7. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  8. If f(x) = |1 -x|, then the points where sin^-1 (f |x|) is non-differen...

    Text Solution

    |

  9. Let f(x)=1/(1+e^(1/x))for\ x!=0\ a n d\ f(0)=0 , then f(0^+) does not ...

    Text Solution

    |

  10. Let f(x)=[(sinx)/x]+[(2sin2x)/x]++[(10sin10 x)/x] (where [.] is the gr...

    Text Solution

    |

  11. In a quadratic equation ax^2 + bx+c= 0 if 'a' and 'c' are of opposite ...

    Text Solution

    |

  12. Let f(x)""=""x|x|""a n d""g(x)""=""s in x Statement 1 : gof is diff...

    Text Solution

    |

  13. Statement 1:(lim)(x->0)sin^(-1){x}\ does not exist (where {.} denot...

    Text Solution

    |

  14. Statement 1: lim(x->0) sqrt(1-cos 2x)/x does not existe . Statement 2...

    Text Solution

    |

  15. Statement 1: If f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i ...

    Text Solution

    |

  16. Statement 1: (lim)(x->0)[x]((e^(1//x)-1)/(e^(1//x)+1)) (where [.] repr...

    Text Solution

    |

  17. Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous ...

    Text Solution

    |

  18. Let f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha ...

    Text Solution

    |

  19. Let f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2dotIf("lim")(xvec1)f(x)e xi s t...

    Text Solution

    |

  20. Given a real valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

    Text Solution

    |