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How do you find the limit of # (x+sinx)/(2x-sinx) # as x approaches infinity?

Answer 1

Emilia Aguilar

#lim_{x->infty}(x+sin(x))/(2x-sin(x)) = 1/2#

#lim_{x->infty}(x+sin(x))/(2x-sin(x)) = lim_{x->infty}(1+sin(x)/x)/(2-sin(x)/x) = 1/2#

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Answer 2

Isabella Ackerman

To find the limit of (x+sinx)/(2x-sinx) as x approaches infinity, we can divide both the numerator and denominator by x. This gives us (1+sin(x)/x)/(2- sin(x)/x). As x approaches infinity, sin(x)/x approaches 0. Therefore, the limit simplifies to 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.