Advanced Math | Proveiff Study

how to Find equilibrium points and plot phase portrait of the following system of differential equations

By SK Math Expert December 15, 2021ODEs

Question : Find equilibrium points and plot phase portrait of the following system of differential equations x’=x(8-4x-y) y’=y(6-x-2y) Solution: Given system of differential equations x'=x(8-4x-y) (1) y'=y(6-x-2y) (2) We shall…

What is gradient ? Write a gradient example

By SK Math Expert December 9, 2021Abstract Algebra, Mathematics, Multivariable Calculus

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…

How do you find gradient of modulus of position vector?

By SK Math Expert December 9, 2021Abstract Algebra, Mathematics, Multivariable Calculus

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…

What is curl of a vector? how do you find curl of position vector ?

By SK Math Expert December 9, 2021Abstract Algebra, Mathematics, Multivariable Calculus

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…

Prove that curl of position vector is zero vector

By SK Math Expert December 9, 2021Abstract Algebra, Mathematics, Multivariable Calculus

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 \[\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\]…

Evaluate the double integral of 3x+7 from x= -5 to 5 and y =0 to sqrt(25-x^2)

By SK Math Expert December 5, 2021Abstract Algebra, Mathematics, Multivariable Calculus

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…

Use method of substitution to Integrate sqrt(25-x^2) from x =-5 to x =5

By SK Math Expert December 5, 2021Abstract Algebra, Mathematics, Multivariable Calculus

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…

Evaluate double integral x = 0 to 3 integral y =x to 3 of (3+xy) dydx

By SK Math Expert December 4, 2021Abstract Algebra, Advanced Math, Mathematics, Multivariable Calculus

Question : Evaluate double integral x = 0 to 3 integral y =x to 3 of (3+xy) dydx Solution : We shall proceed as follows to Evaluate double integral x…

how do you Find curl of vector field (y-z z-x x-y)

By SK Math Expert December 4, 2021Advanced Math

Question : Find curl of vector field (y-z z-x x-y) Solution : To Find curl of vector field (y-z z-x x-y) Given vector field \[F\left(\begin{matrix}x\\y\\z\\\end{matrix}\right)=\left(\begin{matrix}y-z\\z-x\\x-y\\\end{matrix}\right)\] curl of Vector Field F(x,y,z)…

Question : Find divergence of the following Vector Field

By SK Math Expert December 4, 2021Advanced Math

Question : Find divergence of the following Vector Field \[F\left(x,y,z\right)=\left(xyz\ ,\ -yz^2,\ x^2\right)\] Solution : To Find divergence of Vector Field \[F\left(x,y,z\right)=\left(xyz\ ,\ -yz^2,\ x^2z\right)\] Writing this as vector \[F\left(x,y,z\right)=xyz\hat{i}-yz^2\hat{j}+x^2z\hat{k}\]…

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