a) Show that fi (x) = cos x, f2(x) = cos 2x are orthogonal on [-7, n].

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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a) Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7, 1].
b) Find the general solution of the given linear system
dx
= -6x + 2y,
dt
dy
-3x + ly
dt
c) A thin wire of 5 cm length is heated with initial temperature profile f (x) = 1 – x² and
its two ends are kept at a temperature of 0 °C. Assume the thermal diffusivity, k is equal
to 1. Find the temperature distribution in the wire as a function of time. Show all the
intermediate steps.
Transcribed Image Text:a) Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7, 1]. b) Find the general solution of the given linear system dx = -6x + 2y, dt dy -3x + ly dt c) A thin wire of 5 cm length is heated with initial temperature profile f (x) = 1 – x² and its two ends are kept at a temperature of 0 °C. Assume the thermal diffusivity, k is equal to 1. Find the temperature distribution in the wire as a function of time. Show all the intermediate steps.
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