Worksheet 3 Solutions

Out41 0540278 in40 out40 in42 out42 0841468

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Unformatted text preview: 5040 CosTaylor￿x_￿ ￿ 1 ￿ x ^ 2 ￿ 2 ￿ ￿ x ^ 4 ￿ 4 ￿ ￿ x ^ 6 ￿ 6 ￿ 1￿ x2 2 ￿ x4 24 ￿ x6 720 In[41]:= SinTaylor￿1.￿ Out[41]= 0.540278 In[40]:= Out[40]= In[42]:= Out[42]= 0.841468 CosTaylor￿1.￿ Plot￿￿SinTaylor￿x￿, Sin ￿x￿￿, ￿x, ￿ 2 Pi, 2 Pi￿￿ 3 2 1 ￿6 ￿4 ￿2 2 4 6 ￿1 ￿2 ￿3 In[43]:= Out[43]= Plot￿￿CosTaylor￿x￿, Cos ￿x￿￿, ￿x, ￿ 2 Pi, 2 Pi￿￿ 1 ￿6 ￿4 ￿2 2 ￿1 ￿2 ￿3 ￿4 ￿5 ￿6 4 6 3 Problem 2: Taylor series and Euler’s Formula Recall Euler’s formula: For any real number x, eix = cos(x) + i sin(x). We are going to use Euler’s formula to find a Taylor series for ex . (a) Substitute the Taylor series for cos(x...
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