Consider the curve as closed, simple, soft on sections and orientated as shown in the photo (4.0) Considering the no conservative vectorial map provided by F8x,y) = (-y squared, -2xy + 3 cos(3)) by calculating the integral (photo 4.2) we get as a result?

Q: 5. Find an equation plane to the surface (u, v) = (3 cos(u) sin(v), 2 sin(u) sin(v), cos(u)) at the…

A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: 8. For the curve given by r(t)=√√² +8 i + In(t² + 8)j + tk 2 find: a. r'(t)

A: Introduction: For a vector curve rt=ati+btj+ctk, the tangent line at the point of contact t=t0 is…

Q: c) A curve has a parametric equation x = 2t - 1 and y = t* -t'. dy Evaluate dx? 1 at t = 2

A: Given, The parametric equations x=2t3-1, y =t4-t3.

Q: At which point does the parametric curve given by x = 2 cost y = 2 sin t z = 2t - π/3 cross the…

A:

Q: x = 7 te', y = (t + 1)e', 0stsi Set up an integral that represents the area of the surface obtained…

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the given…

A: For the directional derivative first find a unit vector in the direction of θ=π4 then take the the…

Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Question 3. Consider the function f(z, y, z) = 1² + y² +2z2 – 2r – 4y – 8z. The set of points where…

A: Given: f(x,y,z)=x2+y2+2z2-2x-4y-8z (a) To find the parametric equation of the curve containing the…

Q: Eliminate the and write an equation of- carve in part (a) Sobely in cartesian coordinates x, y (e)…

A: As asked we shall solve only part (d) and (e).We have to eliminate the variable t and write the…

Q: Use Green's Theorem to evaluate fa F. dr where F(x, y) = (y cos x, x² + 2y sin x) and C is the…

A:

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

A:

Q: 4. Find the unit tangent vector T(t) to the curve r(t) = (In(cos t), cost, sin t) at time t. (a)…

A:

Q: (3.) (a.) (Circle the correct choice) Which of the following vector functions describes a circle of…

A:

Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: 2. Find a set of parametric equations for the tangent line to the curve of intersection of the…

A: Step 1:To find the parametric equations for the tangent line to the curve of intersection of the…

Q: iez3 dz. ty z – i

A: In this question, we need to find the value of complex integral. Here first we find the contour and…

Q: 16. Sketch the cycloid r(t) = (t- sint, 1 - cos t) together with its tangent vectors at t = and .…

A: Solved the above problem.