I need help with B Resuelva:Consideremos la función f(x) = cosxa. Determinar los polinomios de Maclaurin Po, P2, P4, Pb. Representar en la calculadora ƒ y sus polinomios de Maclaurin citados.c. Evaluar y comparar los valores de f" (0) y Pr (0) paran = 2,4 y 6d. Con los resultados del apartado (c), formular una conjetura sobre f"(0) y Pr (0 Translation:consideringthe function f(x)=cos xa. Determine Maclaurin polynomialsPO,P2,P4,P6.b. Represent in the calculator f and its citedMaclaurin polynomials.c. evaluate and compare values of f^n (0) andp^nn (0) for n= 2,4,6.d. With the results of paragraph (c), make aguess on f^n (0) and p^nn (0).

Answered: Resuelva: Consideremos la función f(x)…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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I need help with B

Resuelva:
Consideremos la función f(x) = cosx
a. Determinar los polinomios de Maclaurin Po, P2, P4, P
b. Representar en la calculadora ƒ y sus polinomios de Maclaurin citados.
c. Evaluar y comparar los valores de f" (0) y Pr (0) paran = 2,4 y 6
d. Con los resultados del apartado (c), formular una conjetura sobre f"(0) y Pr (0

Translation:
considering
the function f(x)=cos x
a. Determine Maclaurin polynomials
PO,P2,P4,P6.
b. Represent in the calculator f and its cited
Maclaurin polynomials.
c. evaluate and compare values of f^n (0) and
p^nn (0) for n= 2,4,6.
d. With the results of paragraph (c), make a
guess on f^n (0) and p^nn (0).

Expert Solution

Step 1

$S o l u t i o n : C o n s i d e r t h e F u n c t i o n : f (x) = c o s (x) A M a c l a u r i n s e r i e s i s g i v e n b y f (x) = \sum_{k = 0}^{n} \frac{f^{(k)} (a)}{k!} x^{k} I n o u r c a s e, f (x) \approx P (x) = \sum_{k = 0}^{n} \frac{f^{(k)} (a)}{k!} x^{k} P (x) = \sum_{k = 0}^{6} \frac{f^{(k)} (a)}{k!} x^{k} S o, w h a t w e n e e d t o d o t o g e t t h e d e s i r e d p o l y n o m i a l i s t o c a l c u l a t e t h e d e r i v a t i v e s, e v a l u a t e t h e m a t t h e g i v e n p o i n t, a n d p l u g t h e r e s u l t s i n t o t h e g i v e n f o r m u l a . P_{0} (x) = f (x) = \cos (x) E v a l u a t e t h e f u n c t i o n a t t h e p o i n t : P_{0} (0) = 1 F i n d t h e 1 s t d e r i v a t i v e : P_{1} (x) = (f (0) (x))' = = - \sin (x) E v a l u a t e t h e 1 s t d e r i v a t i v e a t t h e g i v e n p o i n t : P_{1} (0) = 0 F i n d t h e 2 n d d e r i v a t i v e : P_{2} (x) = (P_{1} (x))' = (- \sin (x))' = - \cos (x) . E v a l u a t e t h e 2 n d d e r i v a t i v e a t t h e g i v e n p o i n t : P_{2} (0) = - 1 F i n d t h e 3 r d d e r i v a t i v e : P_{3} (x) = (P_{2} (x))' = (- \cos (x))' = \sin (x) . E v a l u a t e t h e 3 r d d e r i v a t i v e a t t h e g i v e n p o i n t : P_{3} (0) = 0 F i n d t h e 4 t h d e r i v a t i v e : P_{4} (x) = (P_{3} (x))' = (\sin (x))' = \cos (x) E v a l u a t e t h e 4 t h d e r i v a t i v e a t t h e g i v e n p o i n t : P_{4} (0) = 1 F i n d t h e 5 t h d e r i v a t i v e : P_{5} (x) = (P_{4} (x))' = (\cos (x))' = - \sin (x) E v a l u a t e t h e 5 t h d e r i v a t i v e a t t h e g i v e n p o i n t : P_{5} (0) = 0 F i n d t h e 6 t h d e r i v a t i v e : P_{6} (x) = (P_{5} (x))' = - (\sin (x))' = - \cos (x) E v a l u a t e t h e 6 t h d e r i v a t i v e a t t h e g i v e n p o i n t : P_{6} (0) = - 1 P_{2} (x) = - \cos (x), P_{4} (x) = \cos (x) a n d P_{6} (x) = - \cos (x) P_{2} (0) = - 1, P_{4} (0) = 1 a n d P_{6} (0) = - 1$