EXAMPLE 2 Normal and tangent vectors Let C be the circle x? + y? = a², where a > 0. (х, у) is a. Show that at each point of C, the radial vector field F (x, y) orthogonal to the line tangent to C'at that point. %3D |r| V? + y² (-у,х) V + y? b. Show that at each point of C, the rotation vector field G(x, y) is paralel to the line tangent to C at that point.

Q: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

Q: Given the following relation between x and y answer the following questions. a) Using implicit…

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Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: 6.Consider a function f: R2 R, where f(xy) = cos(xy). Let u = be a unit vector. Use the definition…

A: Here we will use Definition of Directional derivative of f(x , y) in the direction of vector <u1…

Q: 3. If f(x)=3x+2x ,find f'(x), f"(x), f''(x). (Pls use the definition method)

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Q: Consider R = xi +yj+zk and r = a constant vector A = a1 +a2 í + az k: What is (A. V)R in terms of A?…

A: R→=xi→+yj→+zk→ and r=R→, a constant vector A→=a1i→+a2j→+a3k→

Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: Given y2 - 2xy = 1 a) Find y' b) Find y" and make sure your answer y" is in terms of x and y only.

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Q: tangent plane

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Q: 4. Find the unit tangent vector T(t) for the vector function: r(t) = .

A: To find the unit tangent vector.

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A: