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4. Let z=ry". (a) Find əzlər and azdy. (b) Now suppose that I = uv and...
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
Whats the answer to number 1? 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
- bram , July It, 2014 I (a) If z=f(x,y) welt u=x²-yz and U=xy find the Tacoblan of le, U with respect to yy. (b) Use the chain rule to evaluate az and dz When Z= sin ax cosby for x=sity-s-t व
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
Let z equals f left parenthesis x comma y right parenthesis commaz=f(x,y) , where x equals u squared plus v squared and y equals StartFraction u Over v EndFractionx=u2+v2 and y=uv. Find StartFraction partial derivative z Over partial derivative u EndFraction and StartFraction partial derivative z Over partial derivative v EndFraction∂z∂u and ∂z∂v at left parenthesis u comma v right parenthesis equals left parenthesis negative 6 comma negative 6 right parenthesis(u,v)=(−6,−6) , given that : f Subscript x Baseline left parenthesis negative 6 comma...
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of the sphere. Choose the correct answer below. 2 h O A. Compute f(a cos u,a sin u,v)a sin u dv du 0 0 2Tt h O B. Compute f(a cos u,a sin u,v) dv du. 0 0 2 O C. Compute f(a sin u cos v,a sin u sin v,a cos u) dv du. 0 0 2 S. O D. Compute...
Problem 4 Suppose U and V follow uniform [0, 1] independently. (1) Let X = min( UV). Let F(x) = P(X<2). Calculate F(2) and f(c). (2) Let Y = max(U,V). Let F(y) = P(Y = y). Calculate F(y) and f(y). (3) Let Z=U + V. Let F(z) = P(Z < z). Calculate F(2) and f(z).
The contour diagram in Figure 6(a) describes the hyperbolic paraboloid z = f(x, y) = I y. The bold lines represent the r and y axes. (a) (b) Figure 6 i) Through a change of variables u = r+y and v = r-y, show that f can be rewrit- ten in the standard form of a hyperbolic paraboloid. Such a transformation is shown in Figure 6(b) where the bold lines now represent the u and v axes. az ii) Use...