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How do you evaluate the limit #3x^2(2x-1)# as x approaches #-1/2#?

Answer 1

Elijah Abram

It is

#lim_(x->-1/2) 3x^2*(2x-1)=3*(-1/2)^2*(2*(-1/2)-1)=#

#3*(1/4)*(-1-1)=-3/2#

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Answer 2

Scarlett Allison

To evaluate the limit of 3x^2(2x-1) as x approaches -1/2, we substitute -1/2 for x in the expression. By doing so, we get:

3(-1/2)^2(2(-1/2)-1)

Simplifying this expression, we have:

3(1/4)(-1-1/2)

Further simplifying, we get:

3(1/4)(-3/2)

Multiplying the fractions, we have:

3/4 * -3/2

Multiplying the numerators and denominators, we get:

-9/8

Therefore, the limit of 3x^2(2x-1) as x approaches -1/2 is -9/8.

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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.