MAT2002 Lecture : 33-Module_5__The_Strum-Liouvilles_Problem_-_Orthogonality_of_Eigen_functions-07-06-2021_07-Jun-2021

560 Test exercise 7 Write out the solutions carefully. They all quite straightforward. 1 Differentiate the following with respect to x: 38 (b) (Sr +3,- (O cosh, (a) tan 2x sin, 4x er)-3x 2 lfx2 + ,2-2x+2y-23,find/rand얽at the point where x--zy. 4 Ifx-11-cos" and y-3(.-sin") find a and a: in their simple (d) kg.dr.3x-1) sina 田 (x+1 diy when r,y,4ay2以 3 Find an expression for forms Further problems 7 39 1 Differentiate with respect to (b) In(secx+tanx (c) sinxcos'x 2 Find when: a)y-14 cosx if y is a function of x, and x-T+1 show that훑-x(1-x)dr 3 5 Differentiate coshx-1 coshx1 ",.tow. "r-wrmF} o, ,.刍 7 If(x-n'-A(x + y. prove that (2x + y -x+2y. If.e + 2xy + 3,-이.prove that (x + 3 '헒+2tx2 + 2xy + 9 Scanned by CamScanner

Find all eigenvalues and eigenvectors of the matrix Show all your working. Write down a matrix that diagonalises matrix A.