Question

find the value (a) L{sint/


t} (b)​

Answer 1

Answer:

answer

Step-by-step explanation:

The point of the question is to find the Laplace Transform of the Taylor series. Then try to use that to find the Laplace transform of the original function. As you rightly say:

sintt∼1−t23!+t45!−t67!±⋯

The claim then is that

L(sintt)(s)∼L(1−t23!+t45!−t67!±⋯)(s)

The Laplace transform is linear, so we need to find:

L(1)(s)−13!L(t2)(s)+15!L(t4)(s)−17!L(t6)(s)±⋯

Hopefully, you remember that L(tn)(s)=n!/sn+1. So we get:

L(sintt)(s)∼≡≡1s−13!2!s3+15!4!s5−17!6!s7±⋯1s−13s3+15s5−17s7±⋯tan−1(1s)

In the last step I just recognised that

tan−1x∼x−13x3+15x5−17x7±⋯

Answer 2

Answer:

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