Let (1) u(x, y) = xx vx, (2) u(x, y) = In(ex + ey). (3)

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: 2 dydx + f(x, y)dydx

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Q: The field F = xyi+yj-yzk is the velocity field of a flow in space. Find the flow from (0,0,0) to…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: Calculate r' (t) and T(t), where r(t) = (2t - 7,2 – 5t, 3 + 5t). r' (t) = (2 T(t) = -5 5

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

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Q: Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

A: To find f'(t)

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find f '(2), where f (t) = ü(t) · i(t), ü(2) = (1,2,–1), ū'(2) = (3,0,4), and v(t) = (t, t?,t3).

A: To find out the f'(2)

Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

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Q: u = Vx + 5 (x + 1) then du/dx is Зх — 11 Зх + 11 2 Vx + 5 2 Vx + 5 A 3x + 10 Зх — 10 2 Vx + 5 2 Vx +…

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Q: A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is…

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Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

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Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

Q: Display the discontinuity of h at (0,0) and Evaluate hx(0,0).

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Q: Find the extrema of f(x,y)=(x+1)(y+1)(x+y+1)

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Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

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Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

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Q: if f(z)=u(x,y)+iv(x,y)=z^2+3z+4 find u & v

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Q: f(x, y) = V 2 2 3x² + 4y²

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Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: Show that A Yk= V' Yk+r

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Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Q: Let f(x, y) = (5x – y)*. Then %3D дхду Эхдудх dx² dy

A: Partial derivatives: It is a derivative of a function of two or more variables with respect to one…

Q: Find the line integrals of F = 2yi + 4xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where fand g are shown in the figure. Find r'(1) and s'(4).…

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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 the indicated value for f(x,y) = x^2y^3  fxx(1,2) =  fyy(1,2) =  fxy(1,2) =  really…

A: Given query is to find indicated partial derivative.