Limit \(\displaystyle\lim_{{{x}\to{0}}}{\left\lbrace{\frac{{{2}{x}-{\sin{{\left\lbrace{x}\right\rbrace}}}}}{{{3}{x}+{\sin{{\left\lbrace{x}\right\rbrace}}}}}}\right\rbrace}\)

Anika Boyd 2022-03-22 Answered
Limit limx0{2xsin{x}3x+sin{x}}
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Answers (2)

Aarlenlsi1
Answered 2022-03-23 Author has 10 answers
Divide by x!
limx02xsinx3x+sinx=limx02sinxx3+sinxx=213+1=14
where the well-known limit limx0sinxx=1 was used.
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Mercedes Chang
Answered 2022-03-24 Author has 15 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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