`lim_(x -> -oo) (5x^2)/(x + 3)` Find the limit.

Textbook Question

Chapter 3, 3.5 - Problem 25 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Since this is a `(-oo)/(-oo)`  form

Thus, applying L'Hospital's rule we get

`lim_(x->-oo)(5x^2)/(x+3) = lim_(x->-oo) (10x) = -oo`

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scisser | (Level 3) Honors

Posted on

Plug in` -oo` everywhere you have x

`lim_(x->-oo)(5(-oo)^2)/(-oo+3)=(-oo)/-oo `

Since you have , you can use L^Hopital's Rule and differentiate the numerator and denominator independently.

`lim_(x->-oo)10x=-oo `

Therefore,

the `lim_(x->-oo)(5x^2)/(x+3)=-oo `

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