Find e At where 2 5 A= -2 -4
(8') Find the least-squares solution for Az = 5 where 5 and 4 1 A= 2 -1 -2 0 -3 2 -5
Problem 2 (5 pts). Find the Fourier transform of f(x) e", where a is a real number. (Note that your result can be used as a mathematical basis of the uncertainty relation
2. Find the Fourier transform of 3. Find the Fourier transform of re(r), where e(r) is the Heaviside function. 4. Find the inverse Fourier transform of T h, where fe R3 2. Find the Fourier transform of 3. Find the Fourier transform of re(r), where e(r) is the Heaviside function. 4. Find the inverse Fourier transform of T h, where fe R3
(e) Suppose that 4 balls are placed sequentially into one of 5 bins, where the bin for each ball is selected at random. For i = 1, 2,3,4,5, define the indicator variables 1, if the ith bin is empty; 0, otherwise Xi _ Then the number of empty boxes is given by X = X\+X2+ X3 + X4+X5, and we learned from week #7 lecture notes and midterm II that Xi ~ Bernoulli(p) with p = (1 - 2)4 =...
2. Find the derivative of +e= e. State the solution in the form , where a and b contain only positive exponents. Simplify as much as possible.
Find the Limt e tx-e when and when 2) Find the value Co) at 3) show that tue point h point where tue the A Co,0) faSdiun infledio puint 4) Find tue eqution tangedl Line ut o) 5) Shootht 2 is the minima pam Vene funeticn f the pleuse explain tao tu 9 th Find the Limt e tx-e when and when 2) Find the value Co) at 3) show that tue point h point where tue the A Co,0)...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
find L^-1 {2s+4 / s(s^2+4)} 2s+4 Find L s(s2+4) 5 -30 (write 576 by 6 e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t).
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) + arcsin V2x + 4. (b) (a) Set up (but do not evaluate) a definite integral that represents the area 5. of the region R inside the circle r = 4 sin θ and outside the circle r = 2. Carefully sketch the region R. (i)...