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    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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