Home
Class 11
MATHS
Evaluate the following limit: lim(x->2)(...

Evaluate the following limit: `lim_(x->2)(x^2-x-2)/(x^2-2x+"sin"(x-2))`

Text Solution

Verified by Experts

`lim_(x->2)(x^2-x-2)/(x^2-2x+"sin"(x-2))`
`=lim_(x->2)((x-2)(x+1))/(x^2-2x+"sin"(x-2))`
`=lim_(x->2) 1/(x/(x+1)+(sin(x-2))/((x-2)(x+1)))`
`=lim_(x->2)(x+1)(1/(x+(sin(x-2))/(x-2)))`
`=lim_(x->2)(x+1)(1/(lim_(x->2)x+(lim_(x->2)(sin(x-2))/(x-2))))`
`=3(1/(2+1))`
`=1`
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->1)(x^3+x^2-2)/("sin"(x-1))

Evaluate the following limits : lim_(x rarr 2) (x^2-x-2)/ (x^2-3x+2)

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

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

Evaluate the following limits: lim_(xrarr3)((x^(2)-4x)/(x-2))

Evaluate the following limit: (lim)_(x rarr3)(x^(2)-2)/(x+2)

Evaluate the following limits: lim_(xrarr3)((x^(2)-4x+3)/(x^(2)-2x-3))

Evaluate the following limits : lim_(x to 2)(e^(x)-e^(2))/(x-2)

Evaluate the following limits : lim_(x to -2)(1/x+1/2)/(x+2)

Evaluate the following limits: lim_(xrarr0)((2^(x)-1)/(x))

RD SHARMA-LIMITS-All Questions
  1. Evaluate: (lim(n->oo)ncos(pi/(4n))sin(pi/(4n))

    Text Solution

    |

  2. Evaluate the following limit: lim(n->oo)(sin(a/(2^n)))/(sin(b/(2^(n\ )...

    Text Solution

    |

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

    Text Solution

    |

  4. lim(x->1)(1-x)tan(pix)/2=

    Text Solution

    |

  5. The value of lim(x->pi) (sqrt(2+cosx)-1)/(x-pi)^2

    Text Solution

    |

  6. Evaluate the following limit: lim(x->1)(1-1/x)/(sinpi(x-1))

    Text Solution

    |

  7. Evaluate the following limit: lim(x->pi/4)(sqrt(2)-cos x-sin x)/((4x-p...

    Text Solution

    |

  8. Evaluate the following limit: lim(x->pi/4)(cos x-sin x)/((pi/4-x)(cos ...

    Text Solution

    |

  9. Evaluate the following limit: lim(x->pi/4)(1-t a n x)/(1-sqrt(2)sin x)

    Text Solution

    |

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

    Text Solution

    |

  11. Evaluate the following limit: lim(x->pi)(1+cos x)/(tan^2x)

    Text Solution

    |

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

    Text Solution

    |

  13. Evaluate the following limit: lim(x->pi/4)(2-cos e c^2x)/(1-cot x)

    Text Solution

    |

  14. The value of lim(x->pi) (sqrt(2+cosx)-1)/(x-pi)^2

    Text Solution

    |

  15. Evaluate the following limit: lim(x->(3pi)/2)(1+cos e c^3x)/(cot^2x)

    Text Solution

    |

  16. Evaluate: lim(x->e)(logx-1)/(x-e)

    Text Solution

    |

  17. Evaluate the following limit: lim(x->0)(5^x-1)/(sqrt(4+x)-2)

    Text Solution

    |

  18. Evaluate the following limit: lim(x->0)(a^x+b^x-2)/(x^(2\ ))

    Text Solution

    |

  19. Evaluate the following limit: lim(x->0)(8^x-4^x-2^x+1)/(x^2)

    Text Solution

    |

  20. Evaluate the following limit: lim(x->0)(5^x+3^x+2^x-3)/x

    Text Solution

    |