Home
Class 11
MATHS
If lim xto0(x^(-3)sin3x+a x^(-2)+b) exis...

If `lim xto0(x^(-3)sin3x+a x^(-2)+b)` exists and is equal to 0, then (a) `a=-3 and b=9/2` (b) `a=3 and b=9/2` (c) `a=-3 and b=-9/2` (d) `a=3 and b=-9/2`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If lim_(xto0)(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

If f(x)={(|x|-3 when x = 1) & g(x)={2-|x| when x = 2 . if h(x)=f(x)+g(x) is discontinuous at exactly one point, then - (a). a=-3, b=0 (b). a=-3, b=-1 (c) a=2, b=1 (d) a=0, b=1

If lim_(xto0) ((4x-1)^(1/3)+a+bx)/(x)=1/3 then find the values of a and b.

If x+y=k is normal to y^2=12 x , then k is (a)3 (b) 9 (c) -9 (d) -3

(2a^(3)-b^(3))^(3)-b^(9)

If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roots, then a) a=b=c b) a=b!=c c) a=-b=c d) a+b+c=3

If (log)_(10)2=a ,(log)_(10)3=bt h e n(log)_(0. 72)(9. 6) in terms of a and b is equal to (a) (2a+3b-1)/(5a+b-2) (b) (5a+b-1)/(3a+2b-2) (c) (3a+b-2)/(2a+3b-1) (d) (2a+5b-2)/(3a+b-1)

If L=lim_(xto0) (1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exists,then find the value of 1/a - 2/l - 3/b

("lim")_(xto0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equals to (a)1 (b) 0 (c) 2 (d) none of these

Prove that lim_(xto0)(1+3x)^(3/x)=e^(9)

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

    Text Solution

    |

  2. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

    Text Solution

    |

  3. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a)...

    Text Solution

    |

  4. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

    Text Solution

    |

  5. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

    Text Solution

    |

  6. The value of lim(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repre...

    Text Solution

    |

  7. The value of lim(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-...

    Text Solution

    |

  8. The value of underset(xtooo)lim((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((...

    Text Solution

    |

  9. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

    Text Solution

    |

  10. underset(xto1)lim(xsin(x-[x]))/(x-1), where [.] denotes the greatest i...

    Text Solution

    |

  11. underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))], where [.] denotes the gre...

    Text Solution

    |

  12. underset(xtooo)lim(2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

    Text Solution

    |

  13. If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")(xrarrpi/2)f(x)=-oo (b...

    Text Solution

    |

  14. lim(x->-oo)(x^2*tan(1/x))/(sqrt(8x^2+7x+1)) is

    Text Solution

    |

  15. T1 is an isosceles triangle in circle C. Let T2 be another ísoscele...

    Text Solution

    |

  16. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

    Text Solution

    |

  17. lim(xtooo) [((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x) is :

    Text Solution

    |

  18. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e ...

    Text Solution

    |

  19. lim(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 ...

    Text Solution

    |

  20. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

    Text Solution

    |