Home
Class 11
MATHS
Evaluate the following limits: lim(xra...

Evaluate the following limits:
`lim_(xrarr(pi)/(2))(sqrt2-sqrt(1+sinx))/(sqrt2cos^(2)x)`

Text Solution

Verified by Experts

The correct Answer is:
`1/8`
Given limit `=lim_(xto(pi)/(2))((sqrt2-sqrt(1+sinx)))/(sqrt2cos^(2)x)xx((sqrt2+sqrt(1+sinx)))/((sqrt2+sqrt(1+sinx)))`
`=lim_(xto(pi)/(2))(2-(1+sinx))/(sqrt2(1-sin^(2)x))xx(1)/((sqrt2+sqrt(1+sinx)))`
`lim_(x to(pi)/(2))((1-sinx))/(sqrt2(1-sinx)(1+sinx))xx(1)/((sqrt2+sqrt(1+sinx)))`
`=(1)/(sqrt2).lim_(xto(pi)/(2))(1)/((1+sinx)(sqrt2+sqrt(1+sinx)))`
`=(1)/(sqrt2)xx(1)/(2xx2sqrt2)=1/8.`
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

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

Evaluate the following limits: lim_(xrarr(pi)/(4))(1-tanx)/(1-sqrt2sinx)

Evaluate the following limit: (lim)_(x rarr pi/2)(sqrt(2)-sqrt(1+s in x))/(cos^(2)x)

Evaluate the following limits: lim_(xrarr0)((sqrt(1+2x)-sqrt(1-2x)))/(sinx)

Evaluate the following limits: lim_(xrarr0)(sqrt(1+sinx)-1sqrt(1-sinx))/(x)

Evaluate the following limits: lim_(xrarr0)((2x)/(sqrt(x+2)-sqrt(2-x)))

Evaluate the following limit: (lim)_(x rarr2)(x-2)/(sqrt(x)-sqrt(2))

Evaluate the following limits: lim_(xrarr0)((sqrt(2-x)-sqrt(2+x))/(x))

Evaluate the following limits: lim_(xrarr2)((x^(2)-4)/(sqrt(x+2)-sqrt(3x-2)))

Evaluate the following limits: lim_(xrarr4)((3-sqrt(5+x))/(1-sqrt(5-x)))

RS AGGARWAL-LIMIT-EXERCISE 27B
  1. lim(x->pi)(sin(pi-x)/(pi(pi-x)))

    Text Solution

    |

  2. lim(x->pi/2) (tan 2x)/(x-pi/2)

    Text Solution

    |

  3. Evaluate the following limits: lim(xrarr0)(cos2x-1)/(cosx-1)

    Text Solution

    |

  4. Evaluate the following limits: lim(xrarr0)(cosec x-cotx)

    Text Solution

    |

  5. Evaluate the following limits: lim(xrarr0)(1-cos2mx)/(1-cos2nx)

    Text Solution

    |

  6. Evaluate, underset(xrarr0)"lim"(1-cosmx)/(1-cosnx)

    Text Solution

    |

  7. Evaluate the following limits: lim(xrarr0)(sin^(2)mx)/(sin^(2)nx)

    Text Solution

    |

  8. Evaluate the following limits: lim(xrarr0)(sin2x+sin3x)/(2x+sin3x)

    Text Solution

    |

  9. The value of lim(x->0)(sec4x-sec2x)/(sec3x-secx) is

    Text Solution

    |

  10. Evaluate the following limits: lim(x to0)(sqrt2-sqrt(1+cosx))/(2x+si...

    Text Solution

    |

  11. Evaluate the following limits: lim(xrarr0)(sqrt(1+sinx)-1sqrt(1-sinx...

    Text Solution

    |

  12. lim(x->pi/6)(2-sqrt(3)cosx-sinx)/((6x-pi)^2)

    Text Solution

    |

  13. Evaluate the following limits: lim(xrarr0)(cos ax-cos bx)/(cos cx-1)

    Text Solution

    |

  14. Evaluate the following limits: lim(xrarra)(cosx-cosa)/(cotx-cota)

    Text Solution

    |

  15. lim(x rarr pi/4)(tan^3x-tanx)/(cos(x+pi/4)

    Text Solution

    |

  16. Evaluate the following limits: lim(xrarr(pi)/(2))(sqrt2-sqrt(1+sinx)...

    Text Solution

    |

  17. Evaluate the following limit: (lim)(x->pi/6)(cot^2x-3)/(cos e c x-2)

    Text Solution

    |

  18. Evaluate the following limits: lim(xrarr pi)(sqrt(2+cosx)-1)/((pi-x)...

    Text Solution

    |

  19. Evaluate the following limits: lim(xrarr(pi)/(4))(1-tanx)/(1-sqrt2si...

    Text Solution

    |

  20. Evaluate the following limits: lim(x to(pi)/(6))(2sin^(2)x+sinx-1)/(2...

    Text Solution

    |