Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynomials, p„ (x) for the function in sigma notation for S(x) = e" Choose the correct answer. a²x? a²x?_a°x³ Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + P3(x) = 1 + ax + - 2! 3! a²x?¸ a°x³¸ a*xt P4(x) = 1 + ax + P.(x) = 4! ° + 2! 3! k! km0

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 17EQ
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Find the Maclaurin polynomials of orders n =
0,1,2,3, and 4, and then find the nth Maclaurin polynomials, p,(x) for the function in
sigma notation for
f(x) = ex
Choose the correct answer.
a²x?
P3(x) = 1+ ax +
2!
a²x a'x
2!
po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax +
+
3!
a²x? ax?
a*x+
P4(x) = 1+ ax +
2!
4! Pr(x) = :
3!
k!
k=0
Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a²x², p3(x) = 1 + ax + a²x² + a²x³,
P4(x) = 1+ ax + ax + a°x? + a*x*, pn(x) = Ea*x*
k=0
a?x?
P3(x) = 1 –
2
a²x? a°x?
- ax +
Po(x) = 1, p1(x) = 1 – ax, p2(x) =1 - ax +
%3D
a²x? a°x?
РА(х) %3D 1 — ах +
2
Pa(x) = E(-1)*d"x*
3
4
k=0
a²x?
a²x? a°x?
po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax +
P3 (x) = 1+ ax +
2
%3D
P4(x) = 1 + ax +
Pn (x) = E
4
k-0
po(x) = 1, p1(x) = 1 – ax, p2(x) = 1 – ax +
a²x
P3 (x) = 1 – ax +
ax a'x
2!
2!
3!
P4(x) = 1 – ax +
2!
Pu (x) = E(-1ya*xr
3!
4!
k!
k=0
Transcribed Image Text:Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynomials, p,(x) for the function in sigma notation for f(x) = ex Choose the correct answer. a²x? P3(x) = 1+ ax + 2! a²x a'x 2! po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + + 3! a²x? ax? a*x+ P4(x) = 1+ ax + 2! 4! Pr(x) = : 3! k! k=0 Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a²x², p3(x) = 1 + ax + a²x² + a²x³, P4(x) = 1+ ax + ax + a°x? + a*x*, pn(x) = Ea*x* k=0 a?x? P3(x) = 1 – 2 a²x? a°x? - ax + Po(x) = 1, p1(x) = 1 – ax, p2(x) =1 - ax + %3D a²x? a°x? РА(х) %3D 1 — ах + 2 Pa(x) = E(-1)*d"x* 3 4 k=0 a²x? a²x? a°x? po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + P3 (x) = 1+ ax + 2 %3D P4(x) = 1 + ax + Pn (x) = E 4 k-0 po(x) = 1, p1(x) = 1 – ax, p2(x) = 1 – ax + a²x P3 (x) = 1 – ax + ax a'x 2! 2! 3! P4(x) = 1 – ax + 2! Pu (x) = E(-1ya*xr 3! 4! k! k=0
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