If limx→1 x2−ax+bx−1=5, then a+ b is equal to

If limx1x2ax+bx1=5, then a+ b is equal to

  1. A

    5

  2. B

    -4

  3. C

    -7

  4. D

    1

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    Solution:

    Given, limx1x2ax+bx1=5

    For existence of limit, 1a+b=0

     b=a1                                                  …(i)

    limx1x2ax+a1x1=5                               [Using (i)]

    limx1x21a(x1)x1=5limx1(x1)(x+1)a(x1)x1=5limx1(x1)(x+1a)x1=5limx1(x+1a)=52a=5a=3 and b=31=4 [Using (i)] a+b=34=7

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