What does #(x+sin(x))/(x+cos(x))# equal as limit #x-> "infinity"#?? Thank you!!!

Answer 1

1

Divide the numerator and denominator by x, so that given function becomes

#f(x)= (1 + (sin x)/x) / ( 1+ (cos x)/x)#.
Now as #x->oo#. #(sin x)/x ->0#, because sin x would oscillate between +1 and -1, which in either case divided by #oo# would be 0. Thus the limit of the numerator would be 1. Like wise the limit of the denominator would also be 1. Thus limit as a whole would be 1
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Answer 2

The limit of ( \frac{x + \sin(x)}{x + \cos(x)} ) as ( x ) approaches infinity does not exist.

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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.

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.

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.

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.

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