Let w = f(x, y) with f € C² and x = 2k, y = kh³ . Which of the following statements are true? Select all true statements. 3kh? Ow dy dw +h3. ak ду akəh V If w = x – y, then = -3h2. dhək a²w 3kh? 2k- + h3. Əkəh dxðy dy? None of the above

Q: If f(x,y)= Iny, then Vf(x,y)= :- Select one: O True False

A: We know that, gradient is a vector function. ∇fx,y=fxi^+fyj^

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: Express dw and ds interms of rand s, where w = x2 + y?x = r – and y = r +.s = 5rand w as = 38 4rsand…

A: topic - derivatives note : As per bartleby guidelines, we are supposed to answer only first question…

Q: ifwas T!R3-R² Lineartdentifier T(X gy,Z) =(X +2Y +2g0) grand father ☺ KerT ☺ ImI

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Q: Q6. If F(x,y,z) = (x – 3)² + (y – 3)², what is ? 20у - 3) 4 2(х - 3) 2y əy? Q7. V(x, y) = x³ + y³…

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Q: If w = f(x,y), x = uv and y = u + v, find wuy and wWuu:

A: Answer

Q: f(x,y,z) = 6x^2 + 3xy - 2z^3   fx​(x,y,z)= ? fy​(x,y,z)= ? fz​(x,y,z)= ? fyx​(x,y,z)= ?

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Q: If w= Xze' y=va²–x² , z=Sirx, then ( dw is

A: we will derivative by using chain rule

Q: af If f(x) = x²yz + xy³z than is дудz x?yz + xy°z yz + y°z Option 1 Option 2 x? + 3xy? y? + 3xy?…

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Q: If it was G,y) -x+y* Van fy =xy^+ In Ge) @ trae false

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Q: Let f(x, y) = 9e2xy what is fxyx (x, y) =? %3D Select one: O a. 72ye2xy + 72xy²e2xy O b. 36хуе2у +…

A: Given: f(x,y)=9 e2xy ; To find the value of fxyx(x,y)=?

Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: If f(x, y) 3x+7y af then is given by: (3x–7y) 21y (За — 7у)? 21y (3x–7y)² - 42y (За — 7у)2 42y…

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Q: If R=10x3y2z2 and errors in x, y, z are 0.03, 0.01 and 0.02 respectively at x = 3, y = 1, z = 2.…

A: Consider the given formula as R=10x3y2z2. Then, we have…

Q: dy For f vỹ+'Y = vy+/ O y = u^2 O y = u^4 O y = u^(1/2) O y = u^(1/4)

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Q: Let f(x, y) = x²y³, then Vf(1,2)= Select one: True False

A: Given problem:- fx,y=x2y3 Then ∇f1,2=16,12?

Q: If f(x, y) = 7xey + 7y Inx, then is given by: дудх O 49e5y + 7/x 35eby + 7/x O 25e5y + 7/x O 35e5y +…

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Q: 1: Let w = eVE, where x = 5s2 – 4,2, y = 3r?s?, and : = Find the value of when s = 1 and r = 2.

A:

Q: O ди If u = f(x,y), x = g(w) and y = h(w), using Chain Rule, what is aw O ди aw ди Əw || O all of…

A: u=fx,y, x=gw and y=hw

Q: Which of the following is true if* f(x, y) = 2- 2xy + xy³ + 3y? frz (x, y) = 6x fyy (z, y) = 6+ 6xy…

A: Given that f(x,y)= x^3-2xy+xy^3+3y^2 then find the fxx, fyy, fxy.

Q: If f(x,y,z) = e* and g(x,y,z) = y – z Then, V (fg) will be;

A: Given fx,y,z=ex, gx,y,z=y-z

Q: If Cov(x, y) = 0, that means: x and y are dependent. Option 2 f(x,y) = f₁(x)f2(y) Option 1 E(xy) =…

A: We have to tell If cov (x, y) =0 than which option is true.

Q: Let f(x, y)= 3x²y2 , x(t)= t3 and y(t)= t2, then f(x(t), y(t)) is: O 3 t13 O 3t 20 O 3 t12 O 3 t10

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Q: Let w = f(x, y) with f E C² and x =h – kh, y = 4k. Which of the following statements are true?…

A: To find  Which of the given statement is true.

Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

A:

Q: If W (2t – 1, y (t), 4t – 7) = -20, then y (t) = O f +5 O ² +3 O 2 - 5 O ² – 3

A: We will solve this by calculate  wronskian

Q: Let D={(x,y,z) : x2+y2+z?s 49, z2 0}. Evaluate z dv.

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Q: It is always the case that f(x, y) dydx = f(x, y) dædy. OTrue False

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Q: Find ax Je ar az nd 을. if Je 1. 2. f(x. y) = Vy – x´ %3D - 6. f(x. y) = y/x² 8. f(x, y) = V9 – x² –…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Let h(t) = 3t3.2 7t-3.2 %3D | Then h'(t) is h'(1) is s! (7),.4 and h''(1) is

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Q: Q3: van fy = xy*-1 + x",In(x) f(x,y) = x +y* • if it was True false

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Q: If f(x, y) = (x³ + 4y2)3, find and ax ay af Əx af ду II II

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Q: If W=W[y,, y2, y3] where y1, y2 , y3 are twice diffferentiable, W" = W. Select one: O True O False

A: this is true because

Q: If F (s) = (s+2)2+4 , then

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Q: If fx(x)= 1/(1+x²), and fy(y)= 1/(1+y"), X & Y are independent. Find fzw(z,w), if Z-6,5 XY and…

A: Given: fxx=11+x2 fy(y)=11+y2 Determine ∂(z,w)∂(x,y)…

Q: One of the statements below is False.  Which is it:  a, b, c, or  d ? a)  d/dt (t⋅2t) =…

A: We need to find which of the given statement is False. So we will solve each statement and match…

Q: If W= Wly,, Y2, Y3] where y1, y2 , y3 are twice diffferentiable, W" = W. Select one: O True O False

A:

Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: Given: if fx,y,z=x2y2z2 then fxyzx,y,z=2xyzx2y2z2 We have to state if the given statement is true or…

Q: 2. Let fx(X) va+I, Where x > b and a and b are positive parameters. Find E(X) and Var(X).

A: See the handwritten solution

Q: If W= W[y,, y2.Y3] where y1 , y2 , y3 are twice diffferentiable, W" =W. Select one: O True O False…

A:

Q: If f(x, y) = e + e", then .Vf(x, y) = (0, e') :Select one TrueO False

A:

Q: (b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so O on the interval [2, 4] and v(t) > v %3|…

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Q: If f(x, y) = = Select one: O True O False x² + 2xy + y³ 2x + 2y 3y² + 2x '(x² + 2xy + y³)²¹ (x² +…

A: As we know the expression for ∇fx,y. ∇fx,y=i∂∂x+j∂∂yfx,y=∂fx,y∂xi+∂fx,y∂yj   Given: fx,y=1x2+2xy+y3

Q: Let *- y= ÿ.z=0 and x ỹxz= V3 where x,y,ZER'. Which of the followin. 2 can be the value of X Z? V3…

A:

Q: Which of the following is equivalent to the statement "Not all team-mates are friends"? A. O…

A: Introduction: A predicate is a statement or mathematical assertion that includes variables, often…

Q: Q4 * If f(z) = z? ;z = x + iy Show me u(x, y) ;v(x, y) Determine ux; Vy|

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Q: Let S (x,y) = 3e³x² +2e³x+5y + 4e'y?. Find fy A 3e'x4 + 10e³x + 5y + 28e¹y6 12e x³ + 6e³x+5y + 4e¹y7…

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