Advanced Math | Proveiff IT Solutions

What is F(x)F(y) for the given matrix F(x)

By SK Math Expert July 9, 2021Linear Algebraproperties of matrices

Introduction: Here we shall find F(x)F(y) for the given matrix F(x). Question : If \[F(x)\ =\left(\begin{matrix}cos(x)\ &-sin(x)\ &0\\sin(x)&cos(x)&0\\0&0&1\end{matrix}\right)\] then F(x)F(y) is equal to \[F\left(x+y\right)\] \[F\left(x-y\right)\] \[F\left(x\right)+F\left(y\right)\] \[F\left(x\right)-F\left(y\right)\] Solution : Given…

How to find middle terms in the Binomial expansion of (x+a)^(2n+1)

By SK Math Expert July 9, 2021Abstract Algebra, UncategorizedBinomial Expansion

Question : Find middle terms in the Binomial expansion of (x+a)^(2n+1) Solution : Binomial expansion of \[\left(x+a\right)^{2n+1},\ n\in N \] contains 2n+2 terms which is an even number. In the…

how to find middle term in the Binomial expansion of (x+a)^4n

By SK Math Expert July 9, 2021Abstract AlgebraBinomial Expansion

Question : Find middle term in the Binomial expansion of (x+a)^4n Solution : Binomial expansion of \[\left(x+a\right)^{4n},\ n\in N\] contains 4n+1 terms which is an odd number. So the (4n+2)/2…

derivative of the function x^(1/x)

By SK Math Expert July 3, 2021Advanced Mathderivatives

Question : Find the derivative of the function x^(1/x) Solution : Similar Solutions

decreasing function (definition and examples)

By SK Math Expert July 3, 2021Real Analysismonotonic function

Introduction : Here we shall define a decreasing function and strictly decreasing function and provide their examples Similar Solutions Increasing function

increasing function (definition and examples)

By SK Math Expert July 3, 2021Real Analysismonotonic functions

Introduction : Here we shall know about an increasing function and it's examples

If y=1/(1-x^2)^(1/2) then find dy/dx

By SK Math Expert July 3, 2021Advanced Mathdifferentiation

Question : If y=1/(1-x^2)^(1/2) then find dy/dx Solution : Given \[y=\frac{1}{\sqrt{1-x^2}}\] is a rational function. So to find it's derivative, we shall use formula of derivative for a rational function…

what is A intersection (B union C) ?

By SK Math Expert June 29, 2021Advanced Mathalgebra of sets

Question : What is A intersection (B union C) ? Solution : Given A={x:x/2∈Z, 0≤x≤10} => A={0,2,4,6,8,10} B ={x:x is a prime number of one digit} => B ={2,3,5,7} and…