Show that the functions o,(x) = sin(nax²), for n = 1,2,3,..., form are orthogonal set with respect to the “dot" product f•g = [ Ax)g(x)xdx. %3D

Q: The set of functions {sin nx}, n = 1, 2, 3, ... , is %3D orthogonal on the interval [ -n, n]. Show…

A: Given- The set of functions sin nx, n = 1, 2, 3, ⋯, is orthogonal on the interval -π, π To Show-…

Q: 4) Consider the function defined by 10) = /3 (sin (5 + *)) (증+0)) +4 V3 sin (+t) + 4+ V/3 (cos G…

A: we have to show that f(t) is a constant

Q: Test the sets of functions for linear in­dependence in F For those that are linearly dependent,…

A: Given: A set of functions is 1 , sin2x , cos2x. To Find: If the given set of functions are linearly…

Q: Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): =…

A:

Q: „Show that the complex variable function below is differentiable analytic only at origin point? f(z)…

A: We will show the required result.

Q: Write the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r…

A: f(z)=(r+r1​)cosθ+i(r−r1​)sinθ   Explanation:

Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

A:

Q: Differentiate the following function 3 U = ²³² √² + ² + 2 u= +2√+³

A: Derivate with respect to t

Q: Applying any method and show all the steps to determine whether f,(x) = cos 2x f,(x) =1 f,(x) = cosx…

A: We have to solve given question: Concept:

Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

A:

Q: Let Compute dw Əs dw Ət -(-3,-4)= -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A:

Q: Finel the ralves of a anel b such that the function aV5-x tb-1 it Hax cos(TT Ix) 9 +1+ b(x²-7)…

A: Note: There is an error in question, for the given function a has 2 values but it cannot be possible…

Q: Let Compute θω Əs δω Ət -(-3,-4) (-3,-4)= = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A:

Q: Verify by differentiation that

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Q: Which of the following functions maps the red function (y=x)onto the image function? a) y = -x+2|…

A:

Q: Let f = -2x² + 5y² where x cos(t) and y = sin(t). af Ət using the chain rule. Write your answer as a…

A:

Q: Determine whether the function f(z)=z^2+(bar z) is analytical at z=1+i, where (bar z) denotes the…

A: Analytical functions, also known as holomorphic functions, are complex functions that are…

Q: (z)dz

A:

Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: Let Compute θω Əs δώ Ət -(-3,-4) -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A: By chain rule, we will solve the problem.

Q: let (Riae) be aring of real numbar's andf fg Eply R. Such That f= to,,-1,22010-) F-lo-してソの (hoラ-20 )…

A:

Q: 1-x The equation of the tangent line for y = at (- 2, – 3) is 1+X

A: AS PER GUIDELINES I CAN ATTEMPT ONLY FIRST QUESTION

Q: OD Findof the following functions: 1) e" = In(x²y) – y² + 2x* 2) y t = (2x – 3)²

A: Find the derivative of the following function

Q: Any function of the form f(x, y) = ax*y" where a is a real number and k, n are positive integers…

A:

Q: 1. (10 + 7i )®

A:

Q: 4y² Given the function f(x,y)= +e*y _find each of the following. SIMPLIFY

A: Given function is, fx,y=4y2x3+ex2y To find fxy(x,y) Find fxx,y partially differentiating the given…

Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.