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Q: If f(x, y, z) = ln(æ. (1,1, 1). + y° + 2) + V(xº + y8 + 26), then find fr, fy and f; at
A: Here, fx means partial dervative w.r.t. x taking y&z as constants. similar meaning of fy and fz…
Q: 4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z)…
A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…
Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…
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Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…
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Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…
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Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…
A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t and z=1t To express dwdt in terms of t
Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…
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Q: Q2: Expand f(x, y) = [sin (x y*)] about E. 1). Q3: Given T(u) = sin (u), where u = x2 + y2, find…
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Q: Get z = f (x,y), x= es cos t, y= e sin t Show that it's ()" + ()"- az\2 ´əz 2 e* + 1 2 =e2s as. ət.…
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Q: If f(x, y, z) = ln(x6 + yº + 2*) + v(x° + y8 + 2®), then find fe, fy and f; at (1,1,1).
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Q: ( b) For n=1,2,K , show that (x² –1)y"*) +2(nx + p)y") +(n² –n)y"-1) =0 where %3D d" y p") = (Hint:…
A: * Given that y = x+1x-1pa dydx = px+1x-1p-1ddxx+1x-1 dydx = px+1x-1p-1x-11-x+1.1x-12 dydx =…
Q: Consider f(x,y) = cos(x² e³). Then which one of the following is correct O!. fx(x, y) = – 3 y² sin(3…
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Q: 1. x = t, y = 1/(1 +²), z = t² 2. x = cos 4t, y = t, z = sin 4t 3. x = t? – 2, y = t³, z = tª + 1 4.…
A: If any point (x,y,z) on the curve of a function can be represented in terms of a parameter t , then…
Q: Given f(x, y) = sin(x + y) where z s3t0, y = 3s – 6t. Find T = f.(z(s, t), y(s, t)) = f:(x(s, t),…
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Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de
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Q: Get z = f(x,y), x = es cos t, y= es sin t 2 Show that it's ( + )- 2 =e2s 2 + əx. əs
A: Using the chain rule in derivatives, the following proof has been obtained.
Q: Q:Ifx = sin 6, y = 0,y = cos pe, prove that (1-x )y, xy,+p'y= 0, dy where y, dy and y1 d %3!
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Q: dʻz dʻz 2. A. If z = sin(3x +2y) , verify that 2 - ду? = -6z B. If f = x³y³ + 2xcosy + y²lnx then…
A: We have to verify the given equations. This problem can be solved using derivatives.
Q: Q5: Find W,e if W = f(x,y), xr cos6 and y =r sino, then prove that r Wre =-yf + xfy+ xy(fyy-fex) +…
A: The given problem is to find the double partial derivative of the given multi variable function and…
Q: Q2/ Obtain the following: x sin(y) 1) If f(x, y, z) = find fz . z2 9x 2) If f(x, y) = find fy- x2+5y…
A: This is partial derivative so differentiate like normal differentiation but at a time only one…
Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).
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Q: Q1(a) Given that: f(x) = {C (Cos x, 0, os %. 0 <x < n I < x < 2n (a) Sketch extended periodic f(x)…
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Q: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).
A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)
Q: If f(x,y,z)=sin(xy)+x2lny, then fxy at (0,pi/2) is equal to 1 FO
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Q: Find fa, fy, and fz. f (x, y, z) = z In (x'y cos(22)) 5.4 fy = fz =
A: topic - partial differentiation
Q: 3. Find S. F · dr where F(x,y, z) = (3y²e*, 6ye* F(t) = (sin t, ,2-) for 0 <tsn. 1+3) and C is the…
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Q: 2. § F•dï , where F = (ycos(x) – xy sin(x), xy + xcos(x)) and C is the C triangle from (0,0) to…
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Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)
A: It os partial derivative wrt x y z
Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…
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Q: Given f(x, y) = sin(x + y) where r = s°t*, y = 3s – 4t. Find f.(æ(s, t), y(s, t)) = f:(æ(s, t), y(s,…
A: Given, fx,y=sinx+y where x=s3t4 , y=3s-4t
Q: Q2: Expand f(x, y) = [sin (x y³)]? about , 1). Q3: Given T(u) = sin (u), where u = /x2 + y?, find…
A: Concept: " since you have asked multiple question, as per our guidelines we are supposed to solve…
Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))
A: To find the partial derivatives with respect to x ,y ,z.
Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…
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Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…
A: The probability mass function of Y1 and Y2 is,
Q: 6. Evaluate ſe Vf •dr where f(x, y, z) = xy²z³ and r(t) = ti + (r + 1)j + sin (3nt/2)k (0<i< 1)
A: To evaluate∫C∇f·dr where f(x,y,z)=xy2z3 and…
Q: Let z = f(x, y), x = rcos 0 and y = r sin 0. Evaluate the value of zg at the point (x, y) = (/3,1)…
A: Chain rule: If is function of and and are functions of and then, Given:
Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t
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Q: A) F(x,y) = (cos(x+ y) – y sin(x + y), –x sin(x + y)) 1 2т — у B) F(x, y) = ( - x – y’ xy – y² C)…
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Q: Find fæ, fy, and fz. f(z, y, z) = z In(a"y cos(5z) 4.3 = z In (x*y° cos(52)) fr = fy = f: =
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Q: 1- xy xy?+1 A) F(r,v) = (", -) B) F(x, y) = (cos(æ – y) – y sin(x – y), y sin(x – y)) C) F(x, y) =…
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Q: (a) f(r, y) = xª – x²y+y² +6 at P(-1,1) (b) f(r, y) = 2 sin(2x – 3y) at P(0, 7)
A: Please see the explanation below
Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2
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Q: Assuming that the following equations define z an implicit function of x, y and, z = f(x, y), for æ°…
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Q: 2. Which of the following can be differentiated easily without using the Chain Rule? х (b) y = + 2)…
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Q: (g) f (x,y,z) = x² + y? – 2z? + zlnx in P(1,1,1) (h) f(x,y, z) = e*+Ycosz + (y + 1) sin -1x in…
A: Gradient is a vector quantity that represents the rate by which function value is changing. Gradient…
Q: Let f(x, y,2) = x² sin y+y e", where x =t +3,y = ne*-1 and z = In 2t. at t = 1 is: -2 1+2n O -12n…
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Q: If z = x2 – y2 and x = t cos 2r and y = r sin t , then %3D a2z is ar2 (A) 2 cos?(2r) + 2r2 cos?(t) –…
A: Given that,z=x2-y2, x=t cos 2r and y= r sint.Want to find: ∂2z∂r2.
Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…
A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…
Q: At what points (x, y) in the plane are the functions in Exercises 31–33 continuous?
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Q: (22" + e-/") dæ + N (2, y) dy = 0 A) N (x, y) = 12" – pe/v – 3 e-r/y B) N (2, y) = 2" In 2 – In rev²…
A: Given x 2y+e-1ydx + N(x,y)dy = 0 Compare it with Mdx +Ndy = 0 Hence M = x2y+e-1y∂M∂y = x 2y ln2 +…
