GATE EC 2017 Question Paper (05-Feb-2017) (Shift 1)

Let $f\left(x\right)=e^{x+x^2}$ for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which includes all powers of x less than or equal to 3.

A three-dimensional region R of a finite volume is described by

x² + y² ≤ z³ ; 0 ≤ z ≤ 1,

where x, y, z are real. The volume of R (up to two decimal places) is ________.

LetI = $\underset{c}{\int }\left(2zdx+2ydy+2xdz\right)$ where x, y, z are real, and let C be the straight line segment from point A: (0, 2, 1) to point B: (4, 1, –1). The value ofI is ________.

Which one of the following is the general solution of the first order differential equation

$\frac{dy}{dx}={\left(x+y-1\right)}^2$ , where x, y are real?

Starting with x = 1, the solution of the equation x³ + x = 1, after two iterations of Newton-Raphson’s method (up to two decimal places) is ________