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

$$F\left(x\right)=3\cos x+4\sin x,F^{\left(101\right)}\left(\frac{\pi }{2}\right)=?$$

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

$${\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)=3\cos (\mathrm{x}+\frac{\mathrm{n}\pi }{2})+4\sin (\mathrm{x}+\frac{\mathrm{n}\pi }{2})$$$$\Rightarrow {\mathrm{f}}^{\left(101\right)}\left(\frac{\pi }{2}\right)=3\cos (\frac{\pi }{2}+\frac{101\pi }{2})+4\sin (\frac{\pi }{2}+\frac{101\pi }{2})$$$$=3\cos \left(\frac{102\pi }{2}\right)+4\sin \left(\frac{102\pi }{2}\right)$$$$=3\cos \left(51\pi \right)+4\sin \left(51\pi \right)$$$$=3\cos (\pi +50\pi )+4\sin (\pi +50\pi )$$$$=3\cos \left(\pi \right)+4\sin \left(\pi \right)=-3+0=-3$$

Commented by cortano last updated on 20/Nov/21

$$nice$$

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