Home
Class 11
MATHS
Evaluate: ("lim")(xvecpi/2)(1+cos2x)/((p...

Evaluate: `("lim")_(xvecpi/2)(1+cos2x)/((pi-2x)^2)`

Text Solution

Verified by Experts

The correct Answer is:
`1/2`
Putting `(pi-2x)=t,` we have
giving limit `=lim_(t to a)(1+cos(pi-t))/(t^(2))=2/4.lim_(t to0){(sin(t//2))/((t//2))}^(2)=((1)/(2)xx1^(2))=1/2.`
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27C|15 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27A|40 Videos

  • HYPERBOLA

    RS AGGARWAL|Exercise EXERCISE 24|23 Videos

  • LINEAR INEQUATIONS (IN ONE VARIABLE)

    RS AGGARWAL|Exercise EXERCISE 6B|12 Videos

Similar Questions

Explore conceptually related problems

Evaluate: lim_(x rarr(pi)/(2))(1+cos2x)/((pi-2x)^(2))

Evaluate: ("Lim")_(x->0)(1-cosx cos2x cos3x)/(x^2)

lim_ (x rarr pi) (1 + cos x) / ((pi-x) ^ (2))

Evaluate : lim_(x to 0)(1-cos2x)/(3x^(2))

Lim_(x rarr pi/2)(cos x)/((pi)/(2)-x)

Evaluate: lim_(x rarr0)(1-cos2x)/(x^(2))

Evaluate the following: (lim)_(xvecpi/2)(sin x)/x

Evaluate lim_(x to 0) (1 - cos 2x)/(x)

(i) lim_(x to (pi)/(2)) (1+cos 2x)/((pi-2x)^(2)) (ii) lim_( x to 0) (1-cos x.sqrt(cos 2x))/(x^(2)) (iii) lim_(thetararr(pi)/(6)) (sin(theta-(pi)/(6)))/(sqrt(3)-2 cos theta)

Evaluate: lim_(x rarr(pi)/(2))(cos x)^(cos x)

RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarr (pi)/(4))(tanx-1)/((x-(pi)/(...

    Text Solution

    |

  2. lim(x->pi)((sin3x-3sinx)/((pi-x)^3))

    Text Solution

    |

  3. Evaluate: ("lim")(xvecpi/2)(1+cos2x)/((pi-2x)^2)

    Text Solution

    |

  4. Evaluate the following limits: lim(xrarra)((sinx-sina))/((x-a))

    Text Solution

    |

  5. Evaluate the following limits: lim(xrarra)((sinx-sina))/((x-a))

    Text Solution

    |

  6. Evaluate the following limits: lim(xrarra)((sinx-sina))/((sqrtx-sqrta...

    Text Solution

    |

  7. Evaluate the following limits: lim(xrarr0)((sin5x-sin3x))/(sinx)

    Text Solution

    |

  8. Evaluate the following limits: lim(xrarr0)((cos3x-cos5x))/(x^(2))

    Text Solution

    |

  9. Evaluate the following limits: lim(xrarr0)((sin3x+sin5x))/((sin6x-si...

    Text Solution

    |

  10. Evaluate the following limits: lim(xrarr0)([sin(2+x)-sin(2-x)])/(x)

    Text Solution

    |

  11. Evaluate the following limits: lim(xrarr0)((1-cos2x))/((cos2x-cos8x)...

    Text Solution

    |

  12. Evaluate the following limits: lim(xrarr(pi)/(2))((pi)/(2)-x)tanx

    Text Solution

    |

  13. Evaluate the following limits: lim(xrarr0)((sqrt(1+2x)-sqrt(1-2x)))/...

    Text Solution

    |

  14. Evaluate the following limits: lim(xrarr0)((e^(tan-x)-1))/(tanx)

    Text Solution

    |

  15. Evaluate the following limits: lim(xrarr0)((e^(3+x)-sinx-e^(3)))/(x)

    Text Solution

    |

  16. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(tanx)

    Text Solution

    |

  17. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(x)

    Text Solution

    |

  18. Evaluate the following limits: lim(xrarr0)(ax+x cosx)/(b sinx)

    Text Solution

    |

  19. Evaluate the following limits: lim(xrarr0)(sinax+bx)/(ax+sinbx),wher...

    Text Solution

    |

  20. lim(x->pi)(sin(pi-x)/(pi(pi-x)))

    Text Solution

    |