What happens here?

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1 Answer
MattyMatty
Mar 9, 2018

| sin(x) | <= 1 ," and "arctan(x)/x >= 0

Explanation:

"As "| sin(x) | <= 1", and "arctan(x)/x >= 0, " we have"

| (sin(1/sqrt(x)) arctan(x))/(x sqrt(ln(1+x))) | <= | arctan(x)/(x sqrt(ln(1+x))) |
= arctan(x)/(x sqrt(ln(1+x)))" (both arctan(x)/x and "sqrt(...) >= 0")"
= arctan(x)/(sqrt(x) sqrt(x^-1) x sqrt(ln(1+x)))
= arctan(x)/(sqrt(x) x sqrt(x^-1 ln(1+x)))

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