Question: Find the wrong step and explain why it's wrong. L'Hopital's rule is supposed to be used. lim x0+ x cos(x)/ ln(x) = lim x0+ cos(x)

Find the wrong step and explain why it's wrong. L'Hopital's rule is supposed to be used.

lim x0+ x cos(x)/ ln(x)

= lim x0+ cos(x) x sin(x) /x^1

= lim x0+ (cos(x) x sin(x))/ (x^ 1)^ 1

= lim x0+ (cos(x) x sin(x))x

= lim x0+ xcos(x) x^2sin(x) =

= 0 1 0^2 0 = 0.

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