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What is the limit of #(t^2 - 3)^3(t + 3)^5 # as t approaches -2?

Answer 1

#lim_(trarr-2)(t^2-3)^3(t+3)^5 = color(green)(1)#

As Eddie noted a couple months ago:

If #f(t)=(t^2-3)^3(t+3)^5# since #f(t)# is defined at (and around) #t=-2# #lim_(trarr-2)f(t) = f(-2)# #color(white)("XXXXX")=((-2)^2-3)^3((-2)+3)^5#

#color(white)("XXXXX")=1^3 * 1^5#

#color(white)("XXXXX")=1#

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Answer 2

Isaiah Allen

The limit of (t^2 - 3)^3(t + 3)^5 as t approaches -2 is 0.

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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.

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