Limit \lim_{x\to 0} {\frac{2x-\sin{x}}{3x+\sin{x}}}

bacasauvfl 2022-04-28 Answered
Limit limx0{2xsin{x}3x+sin{x}}
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Answers (2)

louran20z47
Answered 2022-04-29 Author has 14 answers
Divide by x!
limx02xsinx3x+sinx=limx02sinxx3+sinxx=213+1=14
where the well-known limit limx0sinxx=1 was used.
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kweefomucy9
Answered 2022-04-30 Author has 13 answers

Since sinx=x+O(x) for x0 ,your limit becomes: limx02xx+O(x3)3x+xO(x3) thence for x0 the result is 14

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