Home
Class 11
MATHS
Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(sin3x-sin x)/(sinx)`

Text Solution

Verified by Experts

`lim_(x->0)(sin3x-sin x)/(sinx)`
Now apply L Hospital rule
`=lim_(x->0)(d/(dx)(sin3x-sin x))/(d/(dx)(sinx))`
`=lim_(x->0)(3cos3x-cosx)/(cosx)`
`=(3-1)/1`
`=2`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limit: (lim)_(x->0)(e^(sinx)-1)/x

Evaluate the following limits: lim_(xrarr0)((sin5x-sin3x))/(sinx)

Evaluate the following limit: (lim)_(x rarr0)(sin5x-sin3x)/(sin x)

Evaluate of the following limit: (lim)_(x->0)(x-sinx)/(x^3)

Evaluate the following limits: lim_(xrarr0)((sinx-2sin3x+sin5x))/(x)

Evaluate the following limits: lim_(xrarr0)((sin3x+sin5x))/((sin6x-sin4x))

Evaluate the following limits: lim_(xrarr0)((tanx-sinx))/(sin^(3)x)

Evaluate the following limits: lim_(xrarr0)(sin5x)/(sin8x)

Evaluate the following limits: lim_(xrarr0)(sin2x+sin3x)/(2x+sin3x)

Evaluate the following limit: (lim)_(x->0)(e^(sin2x)-e^(sin\ x))/x

RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: lim(x->0)(sin^2 4x^2)/(x^4)

    Text Solution

    |

  2. Evaluate the following limit: lim(x->0)(2x-sin x)/(tanx+x)

    Text Solution

    |

  3. Evaluate the following limit: lim(x->0)(sin3x-sin x)/(sinx)

    Text Solution

    |

  4. Evaluate the following limit: lim(x->0)(cos3x-cos5x)/(x^2)

    Text Solution

    |

  5. Evaluate the following limit: lim(x->0)(sin(2+"x")-"sin"(2-"x"))/"x"

    Text Solution

    |

  6. Evaluate the following limit: lim(x->0)(t a n x-sin x)/(sin3x-x sin x)

    Text Solution

    |

  7. Evaluate the following limit: lim(x->0)(1-cos2x)/(cos2x-cos8x)

    Text Solution

    |

  8. Evaluate the following limit: lim(x->oo) (sin(a+x) + sin(a-x) - 2 sin ...

    Text Solution

    |

  9. Evaluate the following limit: lim(x->0)(x^2+1-cos x)/(xsinx)

    Text Solution

    |

  10. Evaluate the following limit: lim(x->0)(2sin x^0-sin2x^0)/(x^3)

    Text Solution

    |

  11. Evaluate the following limit: lim(x->0)(xtanx)/(1-cos2x)

    Text Solution

    |

  12. Evaluate the following limit: lim(x->0)(cos2x-1)/(cos x-1)

    Text Solution

    |

  13. Evaluate the following limit: lim(x->0)(3sin^2 x-2sinx^2)/(3x^2)

    Text Solution

    |

  14. Evaluate the following limit: lim(x->0)(1-cos4x)/(x^2)

    Text Solution

    |

  15. lim(x->0)(1-cos2x)/(3tan^2x)

    Text Solution

    |

  16. Evaluate the following limit: lim(x->0)(a x+x\ cos x)/(b sinx)

    Text Solution

    |

  17. Evaluate the following limit: lim(x->0)(2sin x-sin2x)/(x^3)

    Text Solution

    |

  18. Evaluate the following limit: lim(x->0)(cos e c x-cot x)/x

    Text Solution

    |

  19. Evaluate the following limit: lim(x->0)(5x+4sin3x)/(4sin2x+7x)

    Text Solution

    |

  20. Evaluate the following limit: lim(x->0)(cos e c x-cot x)

    Text Solution

    |