Advanced Math

Question : What are the two point forward backward and central difference approximations for the first derivative of f at x =8? for the following data set of a values…

Question : solve the following by Cramers rule in matlab x+2y-z=5 -x -2y -3z=7 2x+y-z=-1 Solution: %matlab program to solve x+2y-z=5, -x -2y -3z=7, 2x+y-z=-1 by Cramers rule A =…

Question : Prove that following are divergent sequences (a) an=n/3+1/n (b) bn=n^2-n^3 Solution : A sequence an diverges to +infinity if for any real number a, an > a for…

Question : Prove that the sequence an=(2n-1)/(n+1) converges to 2 Solution: Given sequence \[a_n=\frac{2n-1}{n+1}\] The sequence an converges to a limit 2 if for every \(\epsilon\ > 0\) if there…

Question : Prove that u(x y)=xy+x-y is a harmonic function and find its harmonic conjugate v(x y) Solution : Given the function u(x, y) = xy+x-y Differentiating partially we get…

Question : Solve y''-2y+y=e^(-x) in matlab Solution : >>syms x >>syms y(x) >>ode=diff(y,2)-2*diff(y)+y==e^(-x) ode = (sym) 2 d d -x y(x) - 2⋅──(y(x)) + ───(y(x)) = ℯ dx 2 dx…

Question : Solve y'' - 2y' + y = e^(-x) by variation of parameters method Solution : Given ODE \[y\prime\prime\ -\ 2y\prime\ +\ y\ =\ e^{-x}\] First we shall find…

Question : Prove that 4 * 10^(2n) + 9 * 10^(2n−1) + 5 is divisible by 99 for n ∈ N Solution : We shall apply mathematical induction to Prove…

Question : Prove that 10^(n+1)+10^n+1 is divisible by 3 for n ∈ N Solution : We shall apply mathematical induction to Prove that 10^(n+1) + 10^n + 1 is divisible…