Find f'(t) and f(t). f"(t)=t-cos t, f'(0)=6, f(0)=-6

Tatiana Cook 2022-10-01 Answered
Find f'(t) and f(t).
f"(t)=t-\cos t, f'(0)=6, f(0)=-6
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Answers (1)

Joel Reese
Answered 2022-10-02 Author has 17 answers
f " ( t ) = t cos t , f ( 0 ) = 6 , f ( 0 ) = 6
Integrating both sicles, we have
f ( t ) = t 2 2 sin t + c 1
As f'(0)=6
6 = 0 sin 0 + c 1 c 1 = 6
f ( t ) = t 2 2 sin t + 6
Again Integrating wrt t, we have
f ( t ) = 1 2 t 3 3 + cos t + 6 t + c 2
As f(0)=-6
6 = 0 + cos 0 + 0 + c 2
6 = 1 + c 2 c 2 = 7
f ( t ) = t 3 6 + cos t + 6 t 7
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