10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin v), -3 <u <3, 050 < 27 *** (a) Write a linear equation for the tangent plane to the surface at (0,1,1) (b) Compute the surface area of S.
Rewrite-2 sin(x) + 1 cos (z) as A sin (z + φ) Preview A- Preview Note: φ should be in the interval-π < φ < π
Exercise 9. Solve the BVP a(0, t) = 0 u(r, t)-Uz(n, t) = 0 u(z, 0) = sin z 0<x<π, t>0, t >0 t > 0 (z,0) = 0 2
Problem 4, Find, for 0-x-π, the arc-length of the segment of the curve R(t) = (2 cos t-cos 2t, 2 sin t-sin 2t) corresponding to 0< t < r
3i)16 in polar form: z r(cos 0isin 0) where (1 Write the complex number z and e= The angle should satisfy 0 0 < 2«.
Eliminate the parameter to sketch the curve: 2 = sin -0, 1 y = cos -0, 20, - <O<a
Find the Peano range of the Cauchy problem. Z=38 {r' = (2 = (Z -t)y,-3<t< 3; y(1) = 2
Find all solutions to cos(7a) - cos(a) = sin(4a) on 0 Sa<
QUESTION 4 Suppose a fourth field and path: F= <cos(z), sin(z), xy > and r= <sin(t), cos(t), t-> when Osts 21 What does this field look like? What does the path look like? Find ff. dr (use a calculator), what does it represent? Explain.
Question. Consider () - ( cos(t), sin(t)) for 0 +< 2. Parameterine this curve by are length. Chat