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How do you find the limit of #4 / (x + sin x)# as x approaches infinity?

Answer 1

Paisley Johnson

#lim_(x to oo) 4 / (x + sin x)#

there's not a great deal to do here, i might start with this statement

#= 4 /(lim_(x to oo) (x + sin x))#

and because #sin x in [-1,1] #

#= 4 /(lim_(x to oo) x) = 0#

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Answer 2

Ezra Adams

To find the limit of 4 / (x + sin x) as x approaches infinity, we can use the concept of asymptotes. As x approaches infinity, sin x oscillates between -1 and 1, but it does not have a specific value. Therefore, we can ignore the sin x term and focus on the x term.

As x becomes very large, the x term dominates the expression, and the sin x term becomes negligible. Thus, the limit of 4 / (x + sin x) as x approaches infinity is approximately 0.

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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.