Using the secondary Taylor polynomial P2(x) and the rest of the term R2(x) of the Taylor deployment centered on 0 of e^x, accurately calculate the value of e^0.01 to the sixth decimal place and explain the reason in detail.
Added by James B.
Step 1
The Taylor series expansion of e^x is: e^x = 1 + x + (x^2/2!) + (x^3/3!) + ... To find P2(x), we only need the first three terms of this series: P2(x) = 1 + x + (x^2/2!) P2(0.01) = 1 + 0.01 + (0.01^2/2!) = 1.010050 Show more…
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