(c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

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Q: Let f(x,y)=-x³+4xy-2y²+1; find the critical points of f and test them using D=D(x,y).

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Q: hich z ∈ C the function e^(1/z) is holomorphic?

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Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: Evaluate f fs 2² dS, where S is the portion of x2 + y² + z² = 2 in octant 1.

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Q: Determine the linear approximation of f(x) = x at x = 1. O a. Not in the list О b. у3 3х +2 с. у %3…

A: A detailed solution is given below.

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

A:

Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) > 0.

Q: A function f : R? → R is given by f(x,y) = y² + 2x² – x²y. Find and classify its critical points.

A:

Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: (a) f :Z → Z, where f(x) = x². g : Z → Z, where g(x) = |æ|². %3D (b) f :Z × Z → Z, where f(x, y) =…

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Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: Given f(x, y) = et" Y° – a°y°, show that fæy = fyx· 93 fyæ- %3D

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Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: f(z) =z2 is discontinuous in C

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Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: 8. Find the value of a if F = (axy-z)i+(x+2 yz) j+(y - axz)k is irrotational. %3D

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Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

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Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: Let f (x, y) = r³ + y? – critical points of f . 4xy + 3x + 2y+5. Find and classify all

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Q: 2. Let f(x,y)=xe" and find a) fx, fyr fy

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Q: £f*. S: z = 18, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: The domain of the function f (x, y, z) = In(3xy – 6) is %3D {(x, y) € R² : xy > 2} o {(x, y) E R? :…

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Q: Q = find of るf and るこ for the Ganction f(xz)-ディズ メ+Z

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Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

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Q: Given f(æ, y, z) = 6x² + 3y² + 4z², find f-(x, y, z) = | fy(x, y, 2) = | f:(x, y, z) =

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Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: 1. Given f(x, y) = 4x³y², evaluate f;(1, y) and fy(x, 2).

A: We know that partial derivative of f with respect to x is denoted by fx  and partial derivative of f…

Q: Q3: 1f f(x, y) = 4xCy5 + 6x*y* .Prove that: f(x,y) * fxxyy fxx * fyy = 1

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Q: Q3. If F = x'a, + y'a, + (z² – 1) a̟, find F· dS, where S is defined by r= 2, 0 < z < 2,0 < ¢ < 2r.

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Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: 8. For f(z) = e², find arg f'(z). Use this to verify that lines parallel to the y axis and x axis…

A: Given: f(z)=ez To find: arg(f'(z)) To verify that lines parallel to y-axis and x-axis are mapped…

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: -. Evaluate f. F dr where F(x,y, z) = e²i + xzj+ (x + y)k and C is given by r(t) = t²i + t°j- tk, 0…

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Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: The limit of f (x, y) : as (x,y) approaches (0,0): %3D O Infinity O Doesn't exist Exists and equal…

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Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

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Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

A: