Worksheet 3 Solutions

solution using the rst for terms of the taylor

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Unformatted text preview: s, but with more terms for more accuracy.) Solution: Using the first for terms of the Taylor series, we get the following: sin(1) ≈ 1 − 1 1 1 + − ≈ 0.841468 3! 5! 7! 1 1 1 + − ≈ 0.540278 2! 4! 6! If you use some form of electronic computing device to evaluate sin and cosine at 1, you should get something similar. Using Mathematic, I got: cos(1) ≈ 1 − Sin[1.] = 0.841471 Cos[1.] = 0.540302 (The decimal point tells Mathematica that I want a decimal approximation.) 3 (b) Use a calculator or computer to graph the polynomial equations y = x − x + 3! 2 4 6 y = 1 − x + x − x ? Compare the graphs to those of y = sin(x) and y = cos(x). 2! 4! 6! [If you use a computer, you may turn in a print out of these graphs.] x5 5! − x7 7! and In[37]:= Out[37]= SinTaylor￿x_￿ ￿ x ￿ x ^ 3 ￿ 3 ￿ ￿ x ^ 5 ￿ 5 ￿ ￿ x ^ 7 ￿ 7 ￿ x￿ In[38]:= Out[38]= x3 6 ￿ x5 120 x7 ￿...
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