Calc 2 ( Taylor Series & Mclaurin ) 45min
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MAT 137 – Calculus II Quiz # 10 Name: This quiz is due at the BEGINNING of class on Wednesday, April 8, 2015. Show all work to receive full credit.
1. Consider the function 𝑓 𝑥 = 𝑒!!
! .
a. Use the definition to find the degree 3 Taylor polynomial for 𝑓 𝑥 centered at 𝑐 = 2. Simplify to receive full credit.
𝑓 𝑥 =
b. Use the definition to find the degree 3 Taylor polynomial for 𝑓 𝑥 centered at 𝑐 = 0. Simplify to receive
full credit.
𝑓 𝑥 =
c. Use a known series to find the Taylor series for 𝑓 𝑥 about 𝑥 = 0.
𝑓 𝑥 =
d. Using part c, find the degree 3 Taylor polynomial for 𝑓 𝑥 about 𝑥 = 0. Simplify to receive full credit.
𝑓 𝑥 =
2. Using a known series, find the Taylor series for 𝑓 𝑥 = 𝑥!𝑒!! ! about 𝑥 = 0.
𝑓 𝑥 = 3. Determine a Taylor series about 𝑥 = 0 for the following integral.
sin 𝑥 𝑥
𝑑𝑥
!"# ! !
𝑑𝑥 =
4. Determine a Taylor series about 𝑥 = 0 for the following integral. 1 𝑥 + 𝑒!!
!
𝑥 +
2 1 − 𝑥 !
𝑑𝑥
! ! + !
!!!
! + !
!!! ! 𝑑𝑥 =