8. Let S be the surface r(u, v) = integral F. ds where F(x, y, z) S (tan v, u sin v, u²) where 0 ≤ u ≤ 1 and 0 ≤ v ≤ = xi — yzj. \|4 ㅠ Compute the surface
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- Let S be the surface x2 + y? = 4, 0 < z < x + 2. Compute x dx + y dy + dz.Let C be the curve of intersection of the surface f(x,y) = y2 ex< - 1 and the plane y = 3. Find the slope of the line tangent to curve C at the point on the surface where (x , y) = (1, 3). Enter an integer or a fully reduced fraction such as -2,0, 15 , 3/4 , -7/9 , etc. No Spaces Please.Let h(x, y) = xye-(x²+y²). Classify all local extrema of the surface using the second derivative test.
- 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane at (2, 5, 1) in terms of (u, v) as well as in terms of (x, y, z).Find the surface area of the parametric surface 7(u, v) = (2 cos(2u) + v cos(u), 2 sin(2u) + v cos(u), v sin(u)) where -T < u= Give a parameterization for the surface z ŕ(u, v) = (u, v, = x² - y²: ).Find the surface area of the parametric surface = r(u, v) (u + sin(v), v + sin(u), u-v) where -≤u≤π and T ≤ ≤TT. Enter your answer rounded to 2 decimal places.If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. (7, –7, 10) lies on the level7. Which surface is parameterized by f(u, v) = (u, uv, v) for –1Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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