4. Assuming that the c possible subset of R (c) f(x) = V5 –

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

A:

Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

Q: (c) Compute of using the Chain Rule. of дf дх дf ду дf dz. + дя дх дя ду дя дz дя (Use symbolic…

A:

Q: 10 6) Let g(x) =+ 3 %3D x2 Is g(x) E [3,4], Vx E [3,4]?, using fixed point theorems what can you…

A: First we show that g(3)>4 ,so g(3) does not belongs to [3,4]So we can not say that g(x) is in…

Q: - Let X1, X2, ...,Xn~N(0,0) and T = Fi (T),Var(T)

A:

Q: 3- prove that w = w yx if w = xy² + xy +

A: Given problem:- w=xy2 +x2y3+x3y4  Prove that wxy =wyx

Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

A:

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: 3) Aşağıdaki fonksiyonların tanım bölgelerini bulunuz ve çizimlerini yapınız. Bu fonksiyonların…

A: Given That :   a) z=1+x+y-1+3x-y   , (x0,y0)=(1,2) b) z=sin(x2+y2)x2+y2, (x0,y0)=(0,0) To Find : The…

Q: 1. Let f(x,y, z) = vx + /y- Vz +In(49 – x² – y² – z²). Evaluate f(4, 4, 4).

A: Substitute the values

Q: The critical number(s) of f(r) = (x+ 1)/3 is (are)

A: Given,        The critical numbers of fx=x+113

Q: Given f(x, y, z) = xV/x² - yz - - Determine of дz . O of дz of дz af дz of дz = = x² - у 2√x² - yz…

A: Find the derivative

Q: 1. Let g(x, y) = ev* /x. Evaluate gry and gyæ.

A:

Q: 2. Find three positive integers x, y, and z if their product is 27 and the sum is a minimum.

A: Given three positive numbers are  x, y, and z Product = xyz = 27 And sum is minimum

Q: 9- The general solution for the PDE (DD, + D,D-12D =0 is a. u(x, y) = G,(x)+G,(x+y)+G,(x-y) b. u(x,…

A:

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

A:

Q: Let p(x) = x2/x+2 and p'(x) = x2+4x/(x+2)2 (a) Find all critical values for p(x). Show you work.

A: We have to find

Q: Consider the following problem max f (x) =Σxjn( i=1 subject to x, =1 i=1 2(i-1)x,= (n- 1)d i=1 *, E…

A: note : As per our company guidelines we are supposed to answer ?️only one question. Kindly repost…

Q: 1. Let flxx) = x³ + y3 - 3x2-3y2 - 9y. (a) Find all of the critical points of f.

A: Part (a): (i) Find derivative of x and y. (ii) Equate to zero, to get critical points.

Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

A:

Q: Q1:- Let T =- where W-N(0, 1) and V~xShow that T2-F(1,r).

A: We know that  The ratio of chi-square divided by its degrees of freedom is called the…

Q: In the following cases, show that the p.d.f. of Y is not a member of complete family. 1. Y: N(0, o²)…

A: For any statistics to be a complete statistics it must satisfy the following conditions i) E(x(t)) =…

Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: Let E = XE[0, + 0) } then Sup E Маx E- %3D %3D x+ O True False

A: In this problem we have to determine Sup E and Max E, and check Sup E =Max E is true or false.

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: 1 if i= j 0 otherwise. P:(c;) = 5 is a linearly independent set.

A:

Q: (a) Show that for p> 1, |æ1|P + • .· + |æn|P f(x, t) = tp-1 tp-1 is convex on {(x, t) | t > 0}.

A:

Q: Let f(r, y) = 5x-+ 2y + 4y- 8ay List the critical point:

A:

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

A:

Q: Prove that P (a <X < b) = Fy (b) – Fx (a)

A:

Q: 12. Show that F (x, y, z) = xy +xz + yz has the value 1 if and only if at least two of the variables…

A: This Question is From Boolean algebra where + sign denotes or Operation. So F(x,y,z)=xy + xz+yz if…

Q: show that if Z ~ N(0, 1) and Y ~x²(n) with Z and Y to be independent, then T: n

A:

Q: The critical Points of f(x, y) - x' -3x +3y2-6y are: None of these O (1,1) and (-1,1). O (01) and…

A: We will find the first order partial derivatives of f and equate them to 0 to find the critical…

Q: Show that; is a linearly independent set in R3.

A: S=121,011,201 Let a,b and c be the scalar in R3. Then write the set in term of linear span.…

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

A:

Q: 1 : Determine the manimom and Nalve of the function minimumn x'tyス condition under the *+ 2 7?== 1.

A: To find the absolute maximum and minimum of the function using lagrange multiplier

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

A:

Q: If f(x 1.,„,) = g(ê,e) h(x,...,, then ê is Select one: a. efficient b. consistent C. unbiased d.…

A:

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: If f" (c) > 0 where c is a critical number of f' (x), then (c, f (c)) is a relative maximum of of f…

A:

Q: In C[0, 1], are the functions {x2 , x3 , e2x} linearly independent?

A: Linearly dependent and independent functions: Two differential functions f(x) and g(x) are said to…

Q: 1. State precisely the hypothesis and conclusions of the Squeeze Theorem for the situation in Figure…

A: The squeeze theorem states that

Q: c) Evaluate ſ x*(In x)²dx

A:

Q: 5. Consider the PDE u: +ux - uuy = 0 for - o<x< ∞, - 0<y< ∞, and 0 <t< c with u (0, x, y) = - y.…

A:

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

A: Here, ∂ represents the partial derivative, which means when differentiating with respect to x,…

Q: 1. (12 points) Consider f(x, y) = xy2e". Compute the following: (a) af (b) af dy

A: To find the partial differentiate with respect to x, y remains constant and vice versa.

Q: 7. Let f(r) = 2r - 4r? + 1. %3D (a) Find any critical points (c, f(c)) of f(x).

A: