Find the average of the function f(r,0)=r sin(0/2) over a disk of radius R centered at the origin.

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

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Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find the tangent plane to the equation z = 5x² + 3y² − 3y at the point (5, 4, 161) z =

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Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

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Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Find the tangent vector for the position vector r(t)=ln(1-t)i+(t-t^3)j+e^-3t k

A: Explanation of the answer is as follows