Recent content by ssh

Q. Show that f(z)dz defined in a region is exact if and only if f(z) has a primitive.

Show that a symmetric tensor has n(n+1) \ 2 quantities. In a symmetric tensor we have that Aij = Aji which means that A12 = A21 A23 = A32 and so on. Thus these n quantites are similar. What do we do next?

Can we write this as a Taylor's series as f(x) = Log(1+x), then f'(x)=1\1+x so on.

Show that, \[\tan^{-1}x = xF\left(\frac{1}{2},\, 1,\, \frac{3}{2},\, -x^2\right)\]

Show that, \[\log(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}+\cdots\]

Solve xy'= y using frobenius method The explanation given in the book is very confusing can somebody explain in simple method. Thanks

How to solve \( (x+1) y'' - (2x+5) y' + 2y = (x+1) e^x\) can we assume \(y_1 = (Ax+B) e^x \), then \(y_2= vy_1​\) Is this right? then solve for A and B Finally \( y = c_1 y_1 + c_2 y_2\)

Thanks

To Solve y’’ – 2 y’ – 3y = 64 e-x x ---------------(1) Using the method of undetermined coefficients : The roots of the homogeneous equation are 3 and -1, so the complimentary solution is y = c1 e3x + c2 e-x Then the guess for the particular solution of (1) is e-x x (Ax + B)...

Thanx now its clear

I found this answer in a books, but its very confusing, can some one explain this to me clearly. Ans Since \(f_n \longrightarrow f\) there exists N such that \( \arrowvert f_n(x) - f(x) \arrowvert < \epsilon\) for all n>N and for all x Mn = 1, 2, ... be non - negative real numbers such that...

Q. If each individual function is bounded and if \(f_n\longrightarrow f \) uniformly on S, then prove that {fn} is uniformly bounded on S. Proof : Since each fn is bounded implies \(f_n \leq M_n\) \(\Longrightarrow f_1\leq M_1, f_2 \leq M_2​,\) and so on If M = max {M1, M2,...Mn } then each term...

My question remains unanswered wherever i tried?

This is the question i saw in one of the question papers for which i couldn't find an answer. Let α be of bounded variation on [a,b]. let V(n) be the total variation of α on [a,x] and let V(a)=0 . if f Є R(α), prove that f Є R(V)? If f Є R(α ) then U(P,f,α) – L(P,f,α) < ε right which is...

Is my question unclear or unanswerable?