`lim_(x->oo) (x^2 - x^3)e^(2x)` Evaluate the limit.

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Chapter 4, Review - Problem 11 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`lim_(x->oo)(x^2-x^3)e^(2x)`

`=lim_(x->oo)x^3(1/x-1)e^(2x)`

Apply the Algebraic limit theorem,

`=lim_(x->oo)x^3(lim_(x->oo)1/x-1)lim_(x->oo)e^(2x)`

plug in the value of x

`=oo(0-1)oo`

`=-oo`

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