= Let P denote the path parametrized by r(t): Compute fp F-dr, where F(x, y, z) = (₁) 1). (1), sin (31) 5 cost sin (8t) 0 ≤t≤ 2π.

Q: 21 Let F(x, y) = (3x + 2y)i + (2x - y)j. Evaluate F. dr where C is the curve X y from (0, 0) to (1,…

A: Here we calculate the integral along the curve x = y2 from (0,0) to (1,1)

Q: Calculate dw/du and dwldv using the following functions: = f(x, y, z) = 3x² – 2ry + 4z2 = x(u, v) =…

A: Apply chain rule

Q: Jeremy and Thulile are running toward the point P along two straight paths that make a fixed angle…

A: Given: Jeremy and Thulile are running toward point P along two straight paths that make a fixed…

Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

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Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

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Q: Dat

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Q: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 and equal 1/6 to 1/2 at increments…

A:

Q: f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional…

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Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

A:

Q: The directional derivative of f(1, y) at the point P = (0, 4) in the direction of the origin is -2.…

A: Given directional derivative of fx,y at point P =(0,4) in the direction of O(0,0) is -2. Here,…

Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: /12 5 5 -cost, --sint 13 N(t) = (0, – sin t, - cost) T(t) = 13 13 Let and ||T'(1)||= 13 B(t) . Find…

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Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

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Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: 2. Y=12-36x, Y'co) = 5, 2. dx and yeo) =S. YCx) =?

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Q: Consider the function f(x, y) = x6-7xy and the path r(t) = (cost, sin t). What is the value of…

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Q: What is the af dy of f(x, y) = tan (x²y³ + 2xy)?

A: Topic- Partial differentiationf(x,y)=tan(x2y3+2xy)we know that,ddx(tanx)=sec2xddxxn=nxn-1 We are…

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: The directional derivative of z = f(x, y) at (1,5) in the direction toward the point (7, 4) is 17…

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Q: Definition 3.27 Let P(x, y) be a point in R² and 0 be the radian measure of the angle formed by OP…

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Q: 1 (vz,xz,xy) dr where C is the union of the curve y=x* from (0,0,0) to 1+xyz Evaluate (11,0) and the…

A: