Boundary Value Problem and Rayleigh's Quotient
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8. Consider the boundary value problem (Please view the attachment for proper formatting of this question)
phi'' + lamda*phi = 0
phi(0) - phi'(0) = 0
phi(1) + phi'(1) = 0.
a) Using the Rayleigh quotient, show that lambda > 0.
b) Show that
tan sqrt(lambda) = 2 sqrt(lambda)/(lambda - 1).
Determine the eigenvalues graphically. Estimate the large eigenvalues.
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