Evaluate \(\displaystyle\lim_{{{x}\to{0}^{+}}}{\frac{{{\arccos{{\left({x}\right)}}}-{\frac{{\pi}}{{{2}}}}}}{{{x}{\ln{{\left({x}\right)}}}}}}\)

Rowan Callahan

Rowan Callahan

Answered question

2022-04-04

Evaluate limx0+arccos(x)π2xln(x)

Answer & Explanation

Kingston Lowery

Kingston Lowery

Beginner2022-04-05Added 10 answers

limx0+arccos(x)π2xlnx=limx0+arccos(x)arccos(0)x01lnx=11020=0
It is valid, because if we know that limx0+f(x) and limx0+g(x) exist, then we have that limx0+f(x)g(x) exists and limx0+f(x)g(x)=limx0+f(x)limx0+g(x)

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