Using l'Hospital theorem evaluate the limit of (x^2+11x-12)/(x-1), for x->1.

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We have to find the value of lim x--> 1[ (x^2+11x-12)/(x-1)].

As substituting x = 0 gives us the indeterminate form 0/0, we can use l'Hopital's theorem and substitute the numerator and the denominator with their derivatives.

We get :

lim x--> 1 [2x + 11]

substitute x = 1

...

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We have to find the value of lim x--> 1[ (x^2+11x-12)/(x-1)].

As substituting x = 0 gives us the indeterminate form 0/0, we can use l'Hopital's theorem and substitute the numerator and the denominator with their derivatives.

We get :

lim x--> 1 [2x + 11]

substitute x = 1

=> 2 + 11

=> 13

The value of lim x-->1 [(x^2+11x-12)/(x-1)] = 13.

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