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How do you find the limits of #lim root(3)t +12t-2t^2 where t = -oo#?

#lim root(3)t +12t-2t^2 where t -oo #

Answer 1

Ezra Adams

#lim_(t to-infty) root(3)(t)+12t-2t^2#

#=root(3)(-infty)+12(-infty)-2(-infty)^2#

#=-infty-infty-infty#

#=-infty#

I hope that this was clear.

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Answer 2

William Abdalla

To find the limit of the given expression as t approaches negative infinity, we substitute t = -∞ into the expression:

lim root(3)t + 12t - 2t^2, where t = -∞

Substituting t = -∞ into the expression, we get:

lim root(3)(-∞) + 12(-∞) - 2(-∞)^2

Simplifying further:

lim -∞ + (-∞) - 2(-∞)^2

Since we have -∞ in each term, the limit of the expression as t approaches negative infinity is also -∞.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.