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Limit as x approaches infinity #(3x-2)/(2x+1)#?

Answer 1

#lim_(x->oo)(3x-2)/(2x+1)=3/2#

You can think that when #x# becomes VERY big (say #1,000,000#) you are basically left with #(3,000,000-2)/(2,000,000+1)~=3/2#

to check your result you can evaluate it as:

#lim_(x->oo)(3x-2)/(2x+1)=lim_(x->oo)(x(3-2/x))/(x(2+1/x))=3/2#

Where:

simplify #x#

and remember that when #x->oo#:

#2/x->0# #1/x->0#

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Answer 2

Emily Ammerman

The limit as x approaches infinity of (3x-2)/(2x+1) is 3/2.

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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.