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Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynomials, pn (x) for the function in sigma notation for f(x) = e* Choose the correct answer. O po(x) = 1, p1 (x) = 1 + ax, p2(x) = 1 + ax + a²x², p3(x) = 1 + ax + ax + a°x°, p4(x) = 1 + ax + a²x +a°x? + a*x*, p,(x) = dx %3D k=0 a²x Рз (х) 3D 1 - ах + Po(x) = 1, p1(x) = 1 – ax, p2(x) = 1 – ax + a²x a°x 2 31 2! a²x a*x+ + 3! in P4(x) = 1 – ax + 2! Pn (x) = (-1) k! 4! k=0 po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a²x? P3(x) = 1 + ax + ax a'x %3D 2! 2! 3! a²x a°x d'x + 2! Pn (x) = 2! P4(x) = 1 + ax + %3D 3! 4! k=0 Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a²x P3(x) = 1 + ax + ax ax?

Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynomials, pn (x) for the function in sigma notation for f(x) = e* Choose the correct answer. O po(x) = 1, p1 (x) = 1 + ax, p2(x) = 1 + ax + a²x², p3(x) = 1 + ax + ax + a°x°, p4(x) = 1 + ax + a²x +a°x? + a*x*, p,(x) = dx %3D k=0 a²x Рз (х) 3D 1 - ах + Po(x) = 1, p1(x) = 1 – ax, p2(x) = 1 – ax + a²x a°x 2 31 2! a²x a*x+ + 3! in P4(x) = 1 – ax + 2! Pn (x) = (-1) k! 4! k=0 po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a²x? P3(x) = 1 + ax + ax a'x %3D 2! 2! 3! a²x a°x d'x + 2! Pn (x) = 2! P4(x) = 1 + ax + %3D 3! 4! k=0 Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a²x P3(x) = 1 + ax + ax ax?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
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, pn(x) for the function in sigma notation for f(x) = eax Choose the correct answer. O po(x) = 1, P1 (x) = 1 + ax, p2(x) = 1 + ax + a²x², p3(x) = 1 + ax + a²x + a°x', p4(x) = 1+ ax + a²x² + a°x° + a*x*, p„(x) = a* 3.3 k=0 a²x? Po(x) = 1, p1 (x) = 1 – ax, P2(x) = 1 – ax + 2! a²x P3 (x) = 1 – ax + 2! ax 3!' a²x P4(x) = 1 – ax + 2! a²x a*x+ Pn (x) : n a*x || 3! 4! k! k=0 a²x² po(x) = 1, p1(x) = 1 + ax, p2 (x) = 1 + ax +- 2! a*x* .2 a²x² рз (х) 3D 1 + ах + 2! a²x? 3. %3D 3! a²x? P4(x) = 1 + ax + 2! ax? 3.3 atx Pn (x) = } %3D 3! 4! k! k=0 a²x? a²x 2. a²x? Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + P3(x) = 1 + ax + 2 2.2 3.3 4.4 k.k n
Transcribed Image Text:Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynomials, pn(x) for the function in sigma notation for f(x) = eax Choose the correct answer. O po(x) = 1, P1 (x) = 1 + ax, p2(x) = 1 + ax + a²x², p3(x) = 1 + ax + a²x + a°x', p4(x) = 1+ ax + a²x² + a°x° + a*x*, p„(x) = a* 3.3 k=0 a²x? Po(x) = 1, p1 (x) = 1 – ax, P2(x) = 1 – ax + 2! a²x P3 (x) = 1 – ax + 2! ax 3!' a²x P4(x) = 1 – ax + 2! a²x a*x+ Pn (x) : n a*x || 3! 4! k! k=0 a²x² po(x) = 1, p1(x) = 1 + ax, p2 (x) = 1 + ax +- 2! a*x* .2 a²x² рз (х) 3D 1 + ах + 2! a²x? 3. %3D 3! a²x? P4(x) = 1 + ax + 2! ax? 3.3 atx Pn (x) = } %3D 3! 4! k! k=0 a²x? a²x 2. a²x? Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + P3(x) = 1 + ax + 2 2.2 3.3 4.4 k.k n
a²x? 21: P3(x) = 1 – ax + po(x)% = 1, p1(x) = 1 – ax, p2(x) = 1 – ax + a²x²_a°x? %D | 2! ' 2! 3! a²x² a°x 33 atx+ 4 n a*x* P4(x) = 1 – ax + 2! P2 (x) = (-1)* k! 3! 4! k=0 a²x² a²x² P3(x) = 1 + ax + 2! a°x? a³x³ 3. po(x) = 1, p1(x) = 1 + ax, p2 (x) = 1 + ax + 2! a*x* %3D 3! a²x? P4(x) = 1 + ax + 2! a²x a*x+ 44 n Pn (x) 3! 4! ' k! k=0 a²x? -, P3(x) = 1 + ax + a²x? a°x? Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a³x³ %3D 2 3 a²x² P4(x) = 1 + ax + a²x? a*x+ Pn(x) = .4 a*x* %3D 4 k k=0 a²x? 2 a²x? po(x) = 1, p1 (x) = 1 – ax, p2 (x) = 1 – ax + 2 ax? 3. %3D -, P3 (x) = 1 – ax + 2 | %3D | 2. 3 a²x² p4(x) = 1 – ax + 2 a²x atx 3 Pn(x) = 4 k k=0 3.
Transcribed Image Text:a²x? 21: P3(x) = 1 – ax + po(x)% = 1, p1(x) = 1 – ax, p2(x) = 1 – ax + a²x²_a°x? %D | 2! ' 2! 3! a²x² a°x 33 atx+ 4 n a*x* P4(x) = 1 – ax + 2! P2 (x) = (-1)* k! 3! 4! k=0 a²x² a²x² P3(x) = 1 + ax + 2! a°x? a³x³ 3. po(x) = 1, p1(x) = 1 + ax, p2 (x) = 1 + ax + 2! a*x* %3D 3! a²x? P4(x) = 1 + ax + 2! a²x a*x+ 44 n Pn (x) 3! 4! ' k! k=0 a²x? -, P3(x) = 1 + ax + a²x? a°x? Po(x) = 1, p1(x) = 1 + ax, p2(x) = 1 + ax + a³x³ %3D 2 3 a²x² P4(x) = 1 + ax + a²x? a*x+ Pn(x) = .4 a*x* %3D 4 k k=0 a²x? 2 a²x? po(x) = 1, p1 (x) = 1 – ax, p2 (x) = 1 – ax + 2 ax? 3. %3D -, P3 (x) = 1 – ax + 2 | %3D | 2. 3 a²x² p4(x) = 1 – ax + 2 a²x atx 3 Pn(x) = 4 k k=0 3.
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