Find lim t--> 1[(t^3 – 1)/ (t – 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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