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Question

Solve limx1(2x3)(x1)3x2+3x6

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Solution

We have,


limx1((2x3)(x1)3x2+3x6)



This is 00 form.



So, apply L-Hospital rule,


limx1⎜ ⎜ ⎜ ⎜ ⎜ ⎜(20)(x1)+(2x3)(12x0)6x+30⎟ ⎟ ⎟ ⎟ ⎟ ⎟


limx1⎜ ⎜ ⎜ ⎜ ⎜ ⎜2(x1)+(2x3)(12x)6x+3⎟ ⎟ ⎟ ⎟ ⎟ ⎟


=2(11)+(23)(12)6+3


=129


=118



Hence, the value is 118.


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