1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the helix parameterized by the function ア(t) = Cost i +sin t+tk

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

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Q: 2. Find the equation of the tangent plane to the surface x²+3y²+4z² = 20 (2,2, 1). at the point

A: Step 1:To find the equation of the tangent plane to the surface x2+3y2+4z2=20 at the point (2,2,1),…

Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

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Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: The slope of the curve y =x' + 3x² – 4x+5 at (1,5) is O a. 0 O b. 2 O c. 5 O d. 4

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Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: 7x + 3y xy+1 (a) Compute Vf at the point (2,-4). 1. Let f(x, y) = (b) Compute the derivative of f(x,…

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Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Find the equation of the tangent plane to f(x, y) = x² - 2xy + 5y2 having slope 2 in the positive x…

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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: The slope of the tangent line to the graph of x + y + xy = 3 at (1, 1) is Blank 1. Blank 1 Add your…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Wallis is seated on the line tangent to y=4-3x-x2 at the point (2, -6).

A: wallis is seated on the line  tangent to curve   y=4-3x-x2   at point 2,-6