Home
Class 12
MATHS
lim(xrarr(pi)/2)(1-sinxsin3xsin5xsin7x)/...

`lim_(xrarr(pi)/2)(1-sinxsin3xsin5xsin7x)/(((pi)/2-x)^(2))` is `k` then `k/6` equal to

Text Solution

Verified by Experts

The correct Answer is:
7
`x-(pi)/2=y`
`lim_(yrarr0) (1-cosycose3ycos5ycos7y)/(y^(2))`
`lim_(yrarro) ((sinycos3ycos5ycos7y+3cosysin3ycos5ycos7y),(+5cosycos3ysin5ycos7y+7cosycos3ycos5ysin7y))/(2y)`
`1/2+9/2+25/2+49/2=42`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise MATHEMATICS|263 Videos

Similar Questions

Explore conceptually related problems

lim_(xrarr(pi)/(2)) ((1-sinx)(8x^(3)-pi^(3)))/(pi-2x)^(4)

lim _(xrarr(pi)/(2))(1-sinx)/cos^(2)x =_____

Evaluate lim_(xrarr(pi)/(2))(cosx)/(((pi)/(2)-x)).

The value of lim_(xrarr(pi)/(3))(2-sqrt3sinx-cosx)/((3x-pi)^(2)) is equal to the reciprocal of the number

Evaluate lim_(xrarr(pi)/(6))((sqrt3sinx-cosx))/((x-(pi)/(6))).

lim_(xrarr pi/2) ((1-tanx//2)(1-sinx))/((1-tanx//2)(pi-2x)^3)

lim_(x rarr(pi)/(2))(cot x-cos x)/((pi-2x)^(3)) equals

int_(0)^(pi//4)sin2xsin3xdx

lim_(xrarr0) x^2sin.(pi)/(x) , is

lim_(xrarr(pi))(sinx)/(x-pi) is equal to

RESONANCE-TEST SERIES-MATHEMATICS
  1. Let f(x) be a real valued continuous function on R defined as f(x)=...

    Text Solution

    |

  2. Let all chords of parabola y^(2)=x+1 which subtends right angle at (1,...

    Text Solution

    |

  3. lim(xrarr(pi)/2)(1-sinxsin3xsin5xsin7x)/(((pi)/2-x)^(2)) is k then k/6...

    Text Solution

    |

  4. If derivative of y=|x-1|^(sinx) at x=-(pi)/2 is (1+api)^(b) then value...

    Text Solution

    |

  5. The value of Sin^-1(sin10) is

    Text Solution

    |

  6. f:[0,2pi]rarr[-1,1] and g:[0,2pi]rarr[-1,1] be respectively given by f...

    Text Solution

    |

  7. If solution of cot(sin^(-1)sqrt(1-x^(2)))=sin(tan^(-1)(xsqrt(6))),x!=0...

    Text Solution

    |

  8. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

    Text Solution

    |

  9. One of the diameter of a circle circumscribing the rectangle ABCD is 4...

    Text Solution

    |

  10. Value of limit lim(xrarr0^(+))x^(x^(x)).ln(x) is

    Text Solution

    |

  11. Let A,B and C be square matrices of order 3xx3 with real elements. If ...

    Text Solution

    |

  12. If (a,b) and (c,d) are two points on the whose equation is y=mx+k, the...

    Text Solution

    |

  13. The equation (x)^(2)=[x]^(2)+2x where [x] and (x) are the integers jus...

    Text Solution

    |

  14. Let x^2+y^2+x y+1geqa(x+y)AAx ,y in R , then the number of possible i...

    Text Solution

    |

  15. Let P,Q,R and S be the feet of the perpendiculars drawn from point (1,...

    Text Solution

    |

  16. Let [.] denote G.I.F. and tge0 and S={(x,y):(x-T)^(2)+y^(2)leT^(2) whe...

    Text Solution

    |

  17. A function is defined as f(x)=lim(x->oo)[cos^(2n) x , if x<0) , ...

    Text Solution

    |

  18. If [.] denotes the greatest integer function and x,yepsilonRr,"n" epsi...

    Text Solution

    |

  19. The number of solutions to |e^(|x|)-3|=K is

    Text Solution

    |

  20. Let f(x)={(x+1, -1lexle0),(-x,0ltxle1):} then

    Text Solution

    |