Taylor Polynomial HW
1) Evaluate cos ( 2 π / 3 ) on your calculator and using thefirst 4 terms of the TP for cos x.
2) Integrate cos ( x^3 ), from 0 to π / 6, using the first 3 termsof the TP for cos x.
3) Evaluate e^x at x = .4 on your calculator and using the first 5terms of the TP for e^ x.
4) Integrate e^x3, from 0 to .3, using the first 3 terms of the TPfor ex.
5) If I integrate 1/(1-x) I will get - ln (1 - x). Integrate thegiven TP for 1/(1-x). What is the TP for - ln ( 1 - x )?
6) What is the value of, - ln ( 1 - x ) if x = .3? I got .3567. Usethe first 4 terms of the TP you created in question 5 and see ifyou obtain the same result. I got .3560.
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Here are other Taylor Polynomials for other trig functions:
tan ( x ) = x + (1/3) x3 + (2/15) x5 + (17/315) x7 + (62/2835) x9 +....
sec ( x ) = 1 + (1/2) x2 + (5/24) x4 + (61/720) x6 + ...
7) Find the integral of tan x from 0 to π / 6. Use the first 3terms of the TP.
8) Find a TP for sec 2 x, recall sec 2 x is the derivative of tanx.
9) On your calculator, what is the cos (Ï€ / 3)? You should get 1/2.Obviously, the sec (Ï€ / 3) is 2. Use the first 4 terms of the TPfor sec x and see if the answers agree.
