Q 1: For the matrix A given below
A=\begin{bmatrix}2&0&0\\1&4&0\\3&5&6\end{bmatrix}(a) calculate its eigen values, and (b) determine the eigen vector corresponding to the lowest eigen value.
Q 2: The sum of the infinite series 3+1+\frac13+\left(\frac13\right)^2+\cdots+\left(\frac13\right)^n is
Q 3: \lim\limits_{x\rightarrow\infty}\frac{x^3+1}{2x^2+80x+1} is
Q 4: The value of \int_0^{5\mathrm\pi}\left(2-\sin x\right)dx is
Q 5: The cubic equation x^3-x+10=0 has a root in the interval
Q 6: The Fourier series of the function
f\left(x\right)=\begin{pmatrix}1&0\leq x\leq\mathrm\pi\\-1&-\mathrm\pi<\mathrm x<0\end{pmatrix}extended periodically, f(x+2\pi)=f(x) , is
Q 7: Given f(x,y)=x^2+y^2,\;\nabla^2f is