Maclaurin

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Maclaurin cichy767: Korzystając z rozwinięć Maclaurina funkcji elementarnych obliczyć pochodne: f⁽⁵⁰⁾ (0) ,f(x)=x² cosx

9 mar 19:55

Pytający: Rozwiązanie: https://latex.codecogs.com/gif.latex?%5Cdpi%7B150%7D%20%5Cbg_white%20f%28x%29%3D%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7Bf%5E%7B%28n%29%7D%280%29%7D%7Bn%21%7Dx%5E%7Bn%7D%20%5C%5C%20cosx%3D%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7B%28-1%29%5En%7D%7B%282n%29%21%7Dx%5E%7B2n%7D%5C%5C%20f%28x%29%3Dx%5E2cosx%3Dx%5E2%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7B%28-1%29%5En%7D%7B%282n%29%21%7Dx%5E%7B2n%7D%3D%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7B%28-1%29%5En%7D%7B%282n%29%21%7Dx%5E%7B2n+2%7D%5C%5C%2050%3D2n+2%20%5CRightarrow%20n%3D24%20%5C%5C%20%5Cfrac%7Bf%5E%7B%2850%29%7D%280%29%7D%7B50%21%7Dx%5E%7B50%7D%3D%5Cfrac%7B%28-1%29%5E%7B24%7D%7D%7B%282*24%29%21%7Dx%5E%7B%282*24+2%29%7D%20%5CRightarrow%20f%5E%7B%2850%29%7D%280%29%3D%5Cfrac%7B50%21%28-1%29%5E%7B24%7D%7D%7B48%21%7D%3D49*50%3D2450 Sprawdzenie: http://www.wolframalpha.com/input/?x=0&y=0&i=50-th+derivative+of+x%5E2cosx+where+x%3D0

9 mar 21:14