PYQs Based Test - 11 : Engineering Mathematics

$\underset{n\to \infty }{\lim }\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is _________.

The following table lists an nth order polynomial $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0$ and the forward difference evaluated at equally spaced values of x. The order of the polynomial is

If v is a non-zero vector of dimension 3 × 1, then the matrix A = vv${}^T$ has a rank = _______

The figure shows a shape ABC and its mirror image A₁B₁C₁ across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A₁B₁C₁ is

For k = 0, 1, 2,……, the steps of Newton-Raphson method for solving a non-linear equation is given as

$x_{k+1}=\frac{2}{3}{x}_k+\frac{5}{3}{x}_k^{-2}$

Starting from a suitable initial choice as k tends to ∞, the iterate xₖ tends to