F-x-3cos-x-4sin-x-F-101-pi-2-

Question Number 159719 by tounghoungko last updated on 20/Nov/21

F (x) = 3 \cos x + 4 \sin x, F^{(101)} (\frac{π}{2}) = ?

Answered by mathmax by abdo last updated on 20/Nov/21

f^{(n)} (x) = 3 \cos (x + \frac{n π}{2}) + 4 \sin (x + \frac{n π}{2})

\Rightarrow f^{(101)} (\frac{π}{2}) = 3 \cos (\frac{π}{2} + \frac{101 π}{2}) + 4 \sin (\frac{π}{2} + \frac{101 π}{2})

= 3 \cos (\frac{102 π}{2}) + 4 \sin (\frac{102 π}{2})

= 3 \cos (51 π) + 4 \sin (51 π)

= 3 \cos (π + 50 π) + 4 \sin (π + 50 π)

= 3 \cos (π) + 4 \sin (π) = - 3 + 0 = - 3

Commented by cortano last updated on 20/Nov/21

n i c e

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