Určete Taylorův polynom druhého stupně funkce
f(x)=\sin(5x-\pi)-3. se středem v bodě a=\frac{\pi}{4} .

Question

Určete Taylorův polynom druhého stupně funkce
  f(x)=\sin(5x-\pi)-3.  se středem v bodě   a=\frac{\pi}{4} .

Answer

-3+\frac{\sqrt 2}{2}+\frac{5\sqrt 2}{2}(x-\frac{\pi}{4})-\frac{25\sqrt 2}{4}(x-\frac{\pi}{4})^2

Answer

-3+\frac{\sqrt 2}{2}+\frac{5\sqrt 2}{2}(x+\frac{\pi}{4})-\frac{25\sqrt 2}{2}(x+\frac{\pi}{4})^2

Answer

-3+\frac{\sqrt 2}{2}+\frac{\sqrt 2}{2}(x-\frac{\pi}{4})-\frac{\sqrt 2}{4}(x-\frac{\pi}{4})^2

Answer

-3+\frac{\sqrt 2}{2}-\frac{5\sqrt 2}{2}(x-\frac{\pi}{4})+\frac{25\sqrt 2}{4}(x-\frac{\pi}{4})^2

Answer

-3+\frac{\sqrt 2}{2}+\frac{5\sqrt 2}{2}(x-\frac{\pi}{4})-\frac{25\sqrt 2}{2}(x-\frac{\pi}{4})^2

Answer

-3+\frac{\sqrt 2}{2}+\frac{5\sqrt 2}{2}(x-\frac{\pi}{4})+\frac{25\sqrt 2}{4}(x-\frac{\pi}{4})^2

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