Solve. lim_(t rightarrow 0)(sin kt)/t

Modelfino0g

Modelfino0g

Answered question

2022-09-05

Solve. lim t 0  sin k t t

Answer & Explanation

Dana Chung

Dana Chung

Beginner2022-09-06Added 14 answers

lim t 0  sin k t t weknow that sin t / t = 1 when the limit is approaching 0
sin t t k = 1 k = k
wurpenxd

wurpenxd

Beginner2022-09-07Added 3 answers

lim t 0 ( sin ( k t ) / ( t ) ). If you directly substitute t=0 into the equation, you have the indeterminate form 0/0, so resolve that via L'Hopital's Rule.
= lim t 0 ( sin ( k t ) ) / ( t ) = lim t 0 k cos ( k t ) / 1 = lim t 0 k cos ( k t ) = k cos 0 = k .

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