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How do you find the limit of #(4x^2 -3x+2)/(7x^2 +2x-1)# as x approaches infinity?

Answer 1

Emilia Aguilar

# 4/7#

divide numerator and denominator by the highest exponent of x , in this case # x^2#

hence #( (4x^2)/x^2 - (3x)/x^2 + 2/x^2)/((7x^2)/x^2 + (2x)/x^2 - 1/x^2) #

#= (4 - 3/x +2/x^2)/(7 + 2/x -1/x^2) #

#rArr lim_(x→∞) f(x) = 4/7 # graph{(4x^2-3x+2)/(7x^2+2x-1) [-5.07, 5.067, -2.526, 2.54]}

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Answer 2

Cameron Alexander

To find the limit of (4x^2 - 3x + 2)/(7x^2 + 2x - 1) as x approaches infinity, we can divide both the numerator and denominator by the highest power of x, which is x^2. This gives us (4 - 3/x + 2/x^2)/(7 + 2/x - 1/x^2).

As x approaches infinity, the terms with 1/x and 1/x^2 become negligible compared to the constant terms. Therefore, we can ignore them.

Thus, the limit simplifies to (4/7).

Therefore, the limit of (4x^2 - 3x + 2)/(7x^2 + 2x - 1) as x approaches infinity is 4/7.

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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.