Question

(2x + sin x)/x

What is the limit as x approaches zero?

Answer 1

do you know that sin x ---> x as x --->0 ?

if not I will show below

given that sin x --> x
we have
3x/x = 3

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series for sin x
sin x = x - x^3/3! + x^5/5! ....
as x --0
sin x --> x - much smaller stuff