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

Question

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

4-\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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