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Q: Find f, and f, and evaluate each at the given point. y' f(x, y) = e*y2, (In 4, 2) %3D

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Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

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Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Prove d(x,y) = 8 if x does not equal y and 0 if x equals y is a metric on R, the real numbers.

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Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

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Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: Let z = ety, where x = Vuv and y . Find dz in terms of u and v.

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Q: O Find dyldx if y = x In(x).

A: Given query is to find the value of the derivative.

Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: If (x, y) = (-V3, 1) , then find r and 0.

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: dy let y = xtan z then is da elect

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Q: If z = In /x? + y? , find x- X +y В. 1 С. D. Vx? + y? A.

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Q: . Show that z)= E kz is D: 1215 continuous io domain

A: The series can be shown as continuous in a domain if it converges. Therefore, the first calculate…

Q: Given u(x, t) = t°e¯ï, compute:

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Q: Evaluate ſc(x – y) ds over the path C: F(t) = 4tỉ + 3tj for 0 <t< 2.

A: Given: The curve C: r→t=4ti→+3tj→ for 0≤t≤2 To Evaluate: The integral∫Cx-yds

Q: If S(x, y)= x² +y , find f, and f, . %3D Vr

A: Fx is partial differentiation of F with respect to x.

Q: . If x, y E R with x < y, prove that x < tx + (1 – t)y < y for all t e (0,1).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: If Fu,y, z) = xzi + xyzj =ý k, find v.È %3D ........

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Q: Let z = e*y, where x = Vuv and y = . Find in terms of u and v.

A: Change the z in the terms of u and v and the differentiate.

Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: Given f(z, y) = =* y – z'f, show that fry = fyx-

A: See the attachment

Q: If S e-t)rLnt dt, Find the valae of (n)

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Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: Show that if X and Y are independent rv's, then E(XY) = E(X) · E(Y)

A: we have given that, x and y are independent random variables, then, we will prove, E(XY)= E(X).E(Y),

Q: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: Given f(x, y) = 3x° cos (y"), find f-(r, y) = fy(x, y) = fae (x, y) = fyz (x, y) =

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Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: Let w = 4x? + y? + z? x = psinpcose y= psinpstno z = pcoso Find dw dw dw de ee de

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Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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Q: Let f: X Y and suppose S, {A;}ieI C P(X) and T, {B;}jeJ c P(Y). Show that cn. iel (i) f

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Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

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Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: If // f(x,y) dA > 0. then f(x, y) ≥ 0 for all (x, y) in D. D

A: answer is in next step. please give a like !!

Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: Let F = (x + y) exp(x), x = ln(u), and y = v. Find Your answer should be in terms of , y, U, and v.…

A: We have to find partial derivative

Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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