Určete Taylorův polynom druhého stupně funkce
f(x)=\sin(3x+\frac{\pi}{2})+5. se středem v bodě a=-\frac{\pi}{4} .

Question

Určete Taylorův polynom druhého stupně funkce
  f(x)=\sin(3x+\frac{\pi}{2})+5.  se středem v bodě   a=-\frac{\pi}{4} .

Accepted Answer

5-\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})+\frac{9\sqrt 2}{4}(x+\frac{\pi}{4})^2

Answer

5-\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})+\frac{9\sqrt 2}{2}(x+\frac{\pi}{4})^2

Answer

5+\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})+\frac{9\sqrt 2}{4}(x+\frac{\pi}{4})^2

Answer

5-\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x-\frac{\pi}{4})+\frac{9\sqrt 2}{2}(x-\frac{\pi}{4})^2

Answer

5-\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})-\frac{9\sqrt 2}{4}(x+\frac{\pi}{4})^2

Answer

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

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