Consider the i.v.p X = +2 + Cos(x), Xal = 0. Vevity that the hypotheses of Cauchy Picard theorem for a suitable domatin D 1) fltix)=t²+ Cosa is Continuous vt and x as both t² and cosix) are continuous functions. 2) To check the Lipschitz Condition with respect tox, we compute the partial derivative of fitx) with respect to x. df -Sinc This derivative is bounded VX which means fltix) Satisfies a Lipschizz Condition with respect tox. The hypothesis of the Cauchy Picard thearem is satisfied for the inital Value problem on Some domam D avound t=0. B Then estimate the interval of existence of the Soln.
Consider the i.v.p X = +2 + Cos(x), Xal = 0. Vevity that the hypotheses of Cauchy Picard theorem for a suitable domatin D 1) fltix)=t²+ Cosa is Continuous vt and x as both t² and cosix) are continuous functions. 2) To check the Lipschitz Condition with respect tox, we compute the partial derivative of fitx) with respect to x. df -Sinc This derivative is bounded VX which means fltix) Satisfies a Lipschizz Condition with respect tox. The hypothesis of the Cauchy Picard thearem is satisfied for the inital Value problem on Some domam D avound t=0. B Then estimate the interval of existence of the Soln.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 4CR
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Question
Using Applied Analysis to solve Question 4 Part B.
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