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

1 Answer
bp
Feb 11, 2018

1

Explanation:

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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