sorting - Ordering the following from smallest to largest in terms of efficiency -

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i have tried sort out smallest largest in terms of efficiency got wrong.

any please?

xe, ex, (x+sinx)x20, xe, ln2x, xlnx, x + sinx, 13 + 1/x, lgx, 1/x

could define efficiency? want know how sort these regarding asymptotic complexity? link

when x grow big:

  • 1/x near 0
  • 13 + 1/x near 13
  • lgx grow slow, lg(10000000000) = bit more 33)
  • ln²x slow also, ln²(10000000000) = 530
  • x + sinx approximatively x when x big
  • xlnx
  • x^e x^2.71828
  • (x+sinx)x^20 = x^21 + x^20*sinx, si equal x^21
  • e^x fast growing function, e^20 4.85*10^8

if so, 1/x < 13 + 1/x < lgx < ln²x < x + sinx < xlnx < x^e < (x+sinx)x^20 < e^x


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