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

Evaluate the following limits:
`lim_(xrarr0)([sin(2+x)-sin(2-x)])/(x)`

Text Solution

Verified by Experts

The correct Answer is:
`2cos2`
Given limit `lim_(xto0)(2cos{((2+x+2x))/(2)}sin{((2+x-2+x))/(2)})/(x)`
`=(2cos2)lim_(xto0)(sinx)/(x)=(2cos2)xx1=(2cos2).`
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 the following limits: lim_(xrarr0)(sin4x)/(6x)

Evaluate the following limit: (lim)_(x rarr0)(sin(2+x)-sin(2-x))/(x)

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

Evaluate the following limits: lim_(xrarr0)(sin^(2)mx)/(sin^(2)nx)

Evaluate the following limits: lim_(xrarr0)(x cot2x)

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

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

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

Evaluate the following limits: lim_(xrarr0)(sinxcosx0)/(3x)

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

RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarr0)((cos3x-cos5x))/(x^(2))

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |