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How do you find the limit of #(4x^2)/(x-2)# as x approaches 2?

Answer 1

I think that it diverges giving you:
#lim_(x->2^-)(4x^2)/(x-2)=-oo#
#lim_(x->2^+)(4x^2)/(x-2)=+oo#
By substituting values near #2# from the felt and right I got:

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Answer 2

Elijah Abram

To find the limit of (4x^2)/(x-2) as x approaches 2, we can use direct substitution. However, substituting 2 into the expression results in an undefined value, as the denominator becomes zero. Therefore, we need to simplify the expression before substituting. By factoring the numerator, we get 4x^2 = 4(x)(x). Canceling out the common factor of (x-2) in the numerator and denominator, we are left with 4x/(1). Now, we can substitute 2 into the simplified expression, which gives us 4(2)/(1) = 8. Hence, the limit of (4x^2)/(x-2) as x approaches 2 is 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.