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Find lim t--> 1[(t^3 – 1)/ (t – 1)].  

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tonyah995 | Student, Undergraduate | (Level 1) Salutatorian

Posted December 8, 2010 at 3:11 AM via web

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Find lim t--> 1[(t^3 – 1)/ (t – 1)].

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted December 8, 2010 at 3:13 AM (Answer #1)

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We have to find the value of lim t--> 1[(t^3 – 1)/ (t – 1)]. Now merely replacing the values of x with 1 will yield 0/0 which is indeterminate. Here we can use L’Hopital’s rule, but instead we use another method.

We know that t^3 – 1 = (t -1) (t^2 + t + 1)

lim t--> 1[(t^3 – 1)/ (t – 1)]

Replace t^3 – 1 with (t -1) (t^2 + t + 1)

=> lim t--> 1[(t – 1) (t^2 + t +1)/ (t – 1)]

=> lim t--> 1[(t^2 + t +1)]

Substitute t with 1

=> 1^2 + 1 +1

=> 3

Therefore lim t--> 1[(t^3 – 1)/ (t – 1)] = 3

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