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Original Question
Evaluate the limit. lim x → 1 (ln x)/(sin 5πx)Asked by TayB
Evaluate the limit.
lim x → 1 ln x/sin 5πx
lim x → 1 ln x/sin 5πx
Answers
Answered by
Jai
lim [ ln (x)/(sin (5πx)) ] as x → 1
Use L'hopital's rule. Differentiate numerator and denominator separately:
lim [ (1/x) / 5π(cos(5πx)) ] as x → 1
Substitute x = 1:
= (1/1) / 5π(cos(5π(1)))
= 1 / 5π(-1)
= -1 / 5π
Use L'hopital's rule. Differentiate numerator and denominator separately:
lim [ (1/x) / 5π(cos(5πx)) ] as x → 1
Substitute x = 1:
= (1/1) / 5π(cos(5π(1)))
= 1 / 5π(-1)
= -1 / 5π
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