Let z = g (x, y) = x³ + xy³ + y4 - 6x - 2y + 4, where x = r cos (0) and y дz Use the chain rule to find at (r, 0) =(√2, 7). de

Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: Solve the equation d- = 1- 2X Cof 2X-2 C5 czx 2yCot 2X

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Q: Suppose z = x² sin y, x = -4s² + t², y = -2st. A. Use the chain rule to find and as functions of x,…

A: Given:The functions .To find:The values of:a) b) The numerical values of  at .Concept Used:Power…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

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Q: Eliminate the constant: 3x 3x y=c₁e³x. + + c₂2 ve ³x схе 3 Oy" + 6y' +9y=0 Oy"-6y'+9y=0 Oy"-4y+3y=0…

A: It is given that,y=c1e3x+c2xe3xwe need to eliminate the constants c1 and c2

Q: Use Cramer's rule to solve for y (y only) in x+y=z=6 3x - 2y+z=-5 x + 3y - 2z = 14

A: The given system of linear equations, x+y-z=63x-2y+z=-5x+3y-2z=14 We have to find the value of y…

Q: Consider the function - f(x, y) = 2x² + xy² − 6xy + 5x +2. (a) Show that (1,3) is a stationary point…

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Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: Let f(x, y, 2) =x² + 3r°y? + 2°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: əz Find ( (). If (x, y, z)variables, and (2) a function in (x, y), and achieve the equation: 1 x-2 +…

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Q: Find fzzz for f(x, y) = x²y².

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Q: let r (t) = The y component of r' (5)

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Q: Let f(x, y) = 2x - 5y, r(1) = (cos(t), sin(t)). Use the Chain Rule to calculate f (r(t)) at the…

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

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Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Calculate r' (t) and T(t), where 88.8 r' (t) = ( T(t) = ( r(t) = (3t6,2 - 3t, 2t - 9).

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Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: y? lim (х.у)-(1,0) х2 + у? — 2х + 1

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Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

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Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Given f (x, y) = x cos y - ye*, find fx and fy. Compute Dif (3,-2) and Daf (3,-2) if f(x,y) = 5x3 –…

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Consider the function: f (x,y) = 2x² - 4x - xy² + 2y² - 3. Explain and then use the chain rule for…

A: The given problem is to find the small changes to estimate the change in the function f(x,y) that…

Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1