Abstract Algebra

Question : What is gradient ? Write a gradient example Solution : Gradient Gradient is an vector operator that operates on a scalar function and obtained it's vector differentiation. It…

Question : How do you find gradient of modulus of position vector? Solution : We shall find gradient of modulus of position vector as follows Position vector of an object…

Question : What is curl of a vector? how do you find curl of position vector ?. Solution : Curl : Curl of a vector is an operator that operates…

Question : Prove that curl of position vector is zero vector. Solution : We shall Find curl of position vector as follows We know position vector is represented as \[\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\]…

Question : Evaluate the double integral of 3x+7 from x= -5 to 5 and y =0 to sqrt(25-x^2) \[\int_{x=-5}^{5}{\int_{0}^{\sqrt{25-x^2}}\left(3x+5\right)dydx=}\] Solution : We shall process as follows to Evaluate the double…

Question : Use method of substitution to Integrate sqrt(25-x^2) from x =-5 to x =5 Solution : We shall Use method of substitution to Integrate sqrt(25-x^2) from x =-5 to…