Let f(x, y, z) = 36xz - 14y² and let C be the curve given by r(t) = (1, 42, ) for (1) for 0 ≤1 ≤2. Compute fef (Use symbolic notation and fractions where needed.)

Q: #8. In each case, sketch the set of points determined by the given conditions (a) /2-1+i/>1 (b)…

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Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

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Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: 2. Construct the cubic spline that intersects with function f(x) at these points (1,-5), (0,3),…

A: Given Data: To construct the cubic spline that intersects with function  at the points , ,  and use…

Q: 6. 113° 119 [A] 46 [B] 44 [C] 48 [D] 50 550 (x+25)

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Q: Find the length of the curve: - for 1< y<3. 3 4y 4. x=

A: As we know that the length of a curve x=f(y) is given by:- L=∫ab(f'(y))2+1dy

Q: Let a and b be real numbers. Consider the function y = f(x) = 1x² ax+b For which values of a and b,…

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Q: Prove that the Joukowski map 1 p(2) : (z + maps ONTO T - (-1, 1)

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Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Consider the curve defined by x = 2t – 1 and Y = 2 – t, for –5 <t< 3. Find an equation in X and Y…

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Q: On a grid (x-y plane), a road is designed have a curve defined by f(x) = x² + 2 for 0 ≤ x ≤. Find…

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Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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