Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0, In(2)] → R² with a(t) = (e*,e-2t). I =

Q: Let S be the surface of revolution of the curve C: z? + (y+ 5)² = 4. (a) Find a parametrization of…

A: Consider the given information: Let the surface is given by, z2+(y+52)=4

Q: For an equation " + a? = 0 a) Draw a tangent vector to a solution (2(t), x'(t)) in the phase plane…

A: (a) To solve the given differential equation: Let   p=dxdt, or, x' ⇒dpdt=d2xdt2 ... differentiating…

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: Find X || d'y dx² t' Od²y dr² = for the following parametric functions. y = √t 43/2 4 015/2

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Q: Find the parametrization of the tangent line to the space curve r(t) = (e" , sin(t), (t + 1)-³) at t…

A: Given that  r(t)=(e^(4t),sin(t),(t+1)^(-3)) at t=0 We have to find out the parameterization of the…

Q: Consider the function f : R³ R defined by f(x, y, z) = tanh(5x² + 2y² − 3z²) and the point P : (x,…

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Q: Calculate the line integral of the vector-function F(x, y, z)=(2²+2) i-yzj+xk along the path L: {x=3…

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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: l a parametrization of the surface x³ + 5xy + z² = 10 wh 1 2, y = ,z = 0. e symbolic notation and…

A: In this question, the concept of the equation of the tangent plane is applied. The Equation of…

Q: for the attched r(t): 1) how do I find r'(t) 2) sketch the position vector r(0) 3) sketch the…

A: given that r(t)=e2ti+etj. we need to  : (a) find r'(t) r'(t) is the first derivative of the function…

Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: r(t) = (4+t)i+(9+ln(cos t))k, -pi/2 < t < pi/2 Find principal unit  normal vector N for the curve…

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Q: Consider the function f(x, y) = x³+2xy+y. (a) Give the linearization L(x, y) of f at (2,3). (b) Use…

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