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How do you find the limit #(3x^2+x+2)/(x-4)# as #x->0#?

Answer 1

Emilia Aguilar

#-1/2#

The function is neither undefined/indeterminate for x = 0. Hence we can evaluate the limit by substitution.

#lim_(xto0)((3x^2+x+2)/(x-4))=(0+0+2)/(0-4)=-1/2#

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Answer 2

Emma Aldridge

To find the limit of (3x^2+x+2)/(x-4) as x approaches 0, we can substitute 0 into the expression for x. This gives us (3(0)^2+0+2)/(0-4), which simplifies to (0+0+2)/(-4). Further simplifying, we get 2/-4, which equals -1/2. Therefore, the limit of (3x^2+x+2)/(x-4) as x approaches 0 is -1/2.

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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.

How do you find the limit #(3x^2+x+2)/(x-4)# as #x-&gt;0#?

How do you find the limit #(3x^2+x+2)/(x-4)# as #x->0#?