Solution Found!
a. Find values for the constants a, b, and c that will
Chapter 3, Problem 3AAE(choose chapter or problem)
a. Find values for the constants \(a, b\), and \(c\) that will make
\(f(x)=\cos x \quad \text { and } \quad g(x)=a+b x+c x^{2}\)
satisfy the conditions
\(f(0)=g(0), \quad f^{\prime}(0)=g^{\prime}(0), \quad \text { and } \quad f^{\prime \prime}(0)=g^{\prime \prime}(0)\).
b. Find values for \(b\) and \(c\) that will make
\(f(x)=\sin (x+a) \quad \text { and } \quad g(x)=b \sin x+c \cos x\)
satisfy the conditions
\(f(0)=g(0) \quad \text { and } \quad f^{\prime}(0)=g^{\prime}(0)\)
c. For the determined values of \(a,b\) and \(c\), what happens for the third and fourth derivatives of \(f\) and \(g\) in each of parts (a) and (b)?
Equation Transcription:
Text Transcription:
a,b
c
f(x)=cos x and g(x)=a+bx+cx2
f(0)=g(0), f'(0)=g'(0), and f"(0)=g"(0)
b
c
f(x)=sin (x+a) and g(x)=b sin x+ c cos x
f(0)=g(0) and f'(0)=g'(0)
a,b
c
f
g
Questions & Answers
QUESTION:
a. Find values for the constants \(a, b\), and \(c\) that will make
\(f(x)=\cos x \quad \text { and } \quad g(x)=a+b x+c x^{2}\)
satisfy the conditions
\(f(0)=g(0), \quad f^{\prime}(0)=g^{\prime}(0), \quad \text { and } \quad f^{\prime \prime}(0)=g^{\prime \prime}(0)\).
b. Find values for \(b\) and \(c\) that will make
\(f(x)=\sin (x+a) \quad \text { and } \quad g(x)=b \sin x+c \cos x\)
satisfy the conditions
\(f(0)=g(0) \quad \text { and } \quad f^{\prime}(0)=g^{\prime}(0)\)
c. For the determined values of \(a,b\) and \(c\), what happens for the third and fourth derivatives of \(f\) and \(g\) in each of parts (a) and (b)?
Equation Transcription:
Text Transcription:
a,b
c
f(x)=cos x and g(x)=a+bx+cx2
f(0)=g(0), f'(0)=g'(0), and f"(0)=g"(0)
b
c
f(x)=sin (x+a) and g(x)=b sin x+ c cos x
f(0)=g(0) and f'(0)=g'(0)
a,b
c
f
g
ANSWER:
Solution:
Step 1 of 9:
In this question, we have to find the value of a, b and c according to given condition in inquiry.