EXERCISE 3 (6/32). (a) (2 points) Find the parametric equation of the plane passing through the points P (1,0,0), Q (0,

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Exercise 3 6 32 A 2 Points Find The Parametric Equation Of The Plane Passing Through The Points P 1 0 0 Q 0 1 (33.46 KiB) Viewed 13 times

EXERCISE 3 (6/32). (a) (2 points) Find the parametric equation of the plane passing through the points P (1,0,0), Q (0, 1,0) and S= (0,0,1). Determine a point belonging to the plane and whose distance from P is equal to √2. (b) (1 points) Consider the following parametric surfaces 71(s, t)=<s, scos(t), sin(t)> 72(s, t)=<s, cos(t), sin(t)> 0≤x≤ 1,0 <t<2m 0<<1,0 <t<2x •Draw (s.f) and 72(s, t). •Draw the intersection between the two surfaces. EXERCISE 4 (4/32). Compute the following: (a) (1 point) lim, sa (b) (1 point) f'(z) where f(x) = (c) (2 points) f2re dr (llint: find a function whose derivative is 2re and apply the fundamental theorem of calculus) EXERCISE 5 (6/32) (a) (3 points) Let f(z,y)= cos(1). Compute the cartesian equation of the tangent plane to f(x, y) at the point (/2, 1). (b) (2 points) Let f(z,y)=zcos(y) for 0 ≤ ≤2 and 0≤ y ≤. Draw the intersection between the surface f(z,y) and the plane y = 5. (e) (1 point) f(x,y) = cos(y) for 0≤x≤ 2 and 0 ≤ y ≤ 4. Draw the level curve f(x,y) - 2.