Advanced Math

Question : integral 1 to infinity cos(t)/(x^2+t^2) then which of the following true? Solution :

Question : which of the following true? Solution : consider the function f:R->R For the option (1) If the graph of f intersects some line parallel to x-axis in atleast…

Q. For  α in R  let ⌊α⌋ denotes greatest integer less than or equal to α. Solution : Given function  d:R×R→[0, ∞] defined as  d(x,y)=⌊|x-y|⌋ For the option (1) Suppose…

Problem : Let an be a sequence of positive real numbers Solution : Given a sequence of positive real numbers \[\left\{a_n\right\}_{n\geq0}\]Such that \[K=lim sup _{n\rightarrow\infty}\left|a_n\right|^\frac{1}{n}\]Then by the root test \[\sum_{n=0}^{\infty}{a_nr^n}\]Is…

Question : Find a homogeneous linear differential equation with constant coefficients which is satisfied by the function y = 1 + x + cos^3 x Solution : Given function \[y\…

Question : Show that there does not exist any 4 × 4 real symmetric orthogonal matrix with all diagonal elements zero Solution : Let A be a 4 × 4…

Question : Let a b are integers such that x = 2i+√3 is a solution of the equation x^5 − x^4 + 2x^3 − 2x^2 + ax − b =…

Question : Let x = 2i+√3 be a solution of the equation\[x^5 − x^4 + 2x^3 − 2x^2 + ax − b = 0\]Find the values of a and b…

Identify the domain and the range of the relation (2, 5), (5, 11), (7, 15), (8, 17)  (-2, -1), (-1, -3), (0, -5), (1, -7) 3) (12, 1), (10, 3),…

Question : Find null space of the following vectors and determine linearly dependent or independent? 1. \[\left(\begin{matrix}1\\1\\1\\\end{matrix}\right),\left(\begin{matrix}1\\2\\3\\\end{matrix}\right),\left(\begin{matrix}2\\3\\1\\\end{matrix}\right)\] 2. \[\left(\begin{matrix}-3\\1\\3\\\end{matrix}\right),\left(\begin{matrix}1\\2\\8\\\end{matrix}\right),\left(\begin{matrix}-3\\4\\18\\\end{matrix}\right)\]3. \[\left(\begin{matrix}1\\-2\\1\\\end{matrix}\right),\left(\begin{matrix}2\\1\\0\\\end{matrix}\right),\left(\begin{matrix}3\\0\\1\\\end{matrix}\right)\] Solution : Null space : Null space is the set…