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

Evaluate the following limit: `lim_(x->0)(5x+4sin3x)/(4sin2x+7x)`

Text Solution

Verified by Experts

`lim_(x->0)(5x+4sin3x)/(4sin2x+7x)`
`=lim_(x->0)(5+(4sin3x)/x)/((4sin2x)/x+7)`
`=(5+(lim_(x->0)(4sin3x)/x))/((lim_(x->0)(4sin2x)/x)+7)`
`=(5+4xx1xx3)/(4xx2+7)`
`(5+12)/(8+7)`
`=17/15`
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 limits: lim_(xrarr0)(sin5x)/(sin8x)

Evaluate the following limits: lim_(xrarr0)(sin4x)/(6x)

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

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

Evaluate the following limits: lim_(xrarr0)(tan3x)/(sin4x)

Evaluate the following limit: (lim)_(x->0)(t a n2x-x)/(3x-sin x)

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

Evaluate the following : lim_(x to 0)(sin5x)/(sin3x)

Evaluate the following limit: (lim)_(x->0)(a^(t a n x)-a^(sin x))/(t a n x-sin x),\ a >0

Evaluate the following limits: lim_(xrarr0)(sin(x//4))/(x)

RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: lim(x->0)(2sin x-sin2x)/(x^3)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Evaluate the following limit: (lim)(x->0)(x\ cos x-sin x)/(x^2+t a n x...

    Text Solution

    |

  6. Evaluate the following limit: (lim)(theta->0)(1-cos4theta)/(1-cos6thet...

    Text Solution

    |

  7. Evaluate the following limit: (lim)(theta->0)(sin4theta)/(ta n 3theta)

    Text Solution

    |

  8. Evaluate the following limit: (lim)(x->0)(1-cos5x)/(1-cos6x)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Evaluate the following limit: (lim)(x->0)(sin ax+bx)/(a x+sin bx)

    Text Solution

    |

  12. Evaluate: lim(h->0)((a+h)^2sin(a+h)-a^2sina)/h

    Text Solution

    |

  13. If (lim)(x->0)k x\ cosec\ x=(lim)(x->0) xcosec\ k x , find k

    Text Solution

    |

  14. Evaluate: (lim)(x->pi/2)(cot x)/(pi/2-x)

    Text Solution

    |

  15. Evaluate: (lim)(x->pi/2)(pi/2-x)t a n x

    Text Solution

    |

  16. (lim)(x->pi/2)(tan2x)/(x-pi/2)

    Text Solution

    |

  17. Evaluate the following limits: lim(x->pi/2)(pi/2-x)tanx

    Text Solution

    |

  18. Evaluate the following limit: lim(x->pi/2)(cos^2x)/(1-sin x)

    Text Solution

    |

  19. Evaluate the following limit: (lim)(x->a)(cos x-cos a)/(x-a)

    Text Solution

    |

  20. Evaluate the following limit: (lim)(x->pi/2)(1-sin x)/((pi/2-x)^2)

    Text Solution

    |