Home
Class 12
MATHS
lim(xto0) ((1-cos2x)(3+cosx))/(xtan4xtan...

`lim_(xto0) ((1-cos2x)(3+cosx))/(xtan4xtanx)` is equal to

A

2

B

`(1)/(2)`

C

`4`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(xto0) ((1-cos2x)(3+cosx))/(xtan4tanx)`
` lim_(xto0) ((1-cos2x)/(x^2))((x)/(tan4x))(3+cosx)`
` lim_(xto0) ((2-cos^2x)/(x^2))((1)/(4)xx(4x)/(tan4x))(3+cos x)`
`=2(1)^2xx(1)/(4)xx(3+1)=2`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|101 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

Similar Questions

Explore conceptually related problems

lim_(xto0) ((1-cos2x)(3+cosx))/(xtan4x) is equal to

lim_(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to

(lim)_(xrarr0)((1-cos2x)(3+cosx)/(xtan4x)) is equal to (1) 1/2 (2) 1 (3) 2 (4) -1/4

The value of lim_(xrarr0)(((1-cos4x)(5+cosx))/(xtan5x)) is equal to

The value of lim _(xto0) (cos (sin x )- cos x)/(x ^(4)) is equal to :

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

lim_(xto0)(ae^(2x)-bcosx+c)/(xsinx)=1 then a+b+c is equal to .__________

Lt_(xto0)((1-cos2x)sin5x)/(x^(2)sin3x) is equal to (i) (6)/(5) (ii) 5/6 (iii) 10/3 (iv) 3/10

lim_(xto0)(1-cos(x^(2)))/(x^(3)(4^(x)-1)) is equal to:

Evaluate lim_(xto0) (cosx)^(cotx).

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. lim(xto0) ((1-cos2x)(3+cosx))/(xtan4xtanx) is equal to

    Text Solution

    |

  2. Let f(x)={(x^(2),x epsilonZ),((d(x^(2)-4))/(2-x),x !inZ):} the set of ...

    Text Solution

    |

  3. If Sn=sum(k=1)^n ak and lim(n->oo)an=a , then lim(n->oo)(S(n+1)-Sn)/sq...

    Text Solution

    |

  4. If a1=1a n da(n+1)=(4+3an)/(3+2an),ngeq1,a n dif("lim")(nvecoo)an=a , ...

    Text Solution

    |

  5. If x(1)=3 and x(n+1)=sqrt(2+x(n))" ",nge1, then underset(ntooo)limx(n)...

    Text Solution

    |

  6. The value of underset(xrarr0)(lim)(sqrt(1-cosx^(2)))/(1-cos x) is

    Text Solution

    |

  7. Evaluate underset(ntooo)limncos((pi)/(4n))sin((pi)/(4n)).

    Text Solution

    |

  8. Evaluate ("lim")(n→oo){cos(x/2)cos(x/4)cos(x/8)... cos(x/(2^n))}

    Text Solution

    |

  9. If f(x) is the integral of (2 sin x - sin 2x )/(x ^ 3 ) , w...

    Text Solution

    |

  10. Evaluate: ("lim")(xvec0)x^m(logx)^n ,m , n in Ndot

    Text Solution

    |

  11. The value of lim(xrarroo) (logx)/(x^n), n gt 0, is

    Text Solution

    |

  12. underset(xtoa)lim(log(x-a))/(log(e^(x)-e^(a)))

    Text Solution

    |

  13. Let < an > be a sequence such that lim(x->oo)an=0. Then lim(n->oo)(a1...

    Text Solution

    |

  14. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of ("l...

    Text Solution

    |

  15. If f(9)=9,f^(prime)(9)=4,t h e n("lim")(nvecoo)(sqrt(f(x)-3))/(sqrt(x-...

    Text Solution

    |

  16. A(i)=(x-a(i))/(|x-a(i)|),i=1,2,...,n," and "a(1)lta(2)lta(3)lt...lta(n...

    Text Solution

    |

  17. lim(x -> oo) x^n / e^x = 0, (n is an integer) for

    Text Solution

    |

  18. lim(xrarr0) (x)/(tan^-1x) is equal to

    Text Solution

    |

  19. If f(x) =x , x<0 and f(x)=1 , x = 0, and f(x)=x^2,x>0 then lim(x->0) ...

    Text Solution

    |

  20. Evaluate the following limits : Lim(x to oo) sqrt(((x+sin x)/(x- cos...

    Text Solution

    |

  21. Evaluate: ("lim")(xvecoo)(1+1/(a+b x))^(c+dx),w h e r ea , b , c ,a n ...

    Text Solution

    |