Problem 3 (10pt). Let R be the portion of the plane x+y+z = 1 in the first octant (i.e, x,y,z > 0). Compute the surface integral xds.

Problem 5 (10pt). Let F = xyi - zj and R is the unit square in the xy-plane, {0 < x,y≤1,z=0}. Compute curlF ds = c curlF.NdS where N is the unit upward normal vector to R.

Problem 6 (10pt). R Use divergence theorem to calculate the surface integral f√ F. ds = √ √ F. Nds where N is the unit outward normal vector, F = x²i – x³z²j – 4x³zk, and R is the closed surface bounded by the cylinder x² + y² = 1 and planes z = x + 2 and z = = 0.

Problem 2 (10pt). Let F = xyzi+yzj + zk. Compute the divergence and curl of F.

The Fibbonacci sequence is defined recursevely as following for i≥3 FiFi-1+ Fi-2; F1 = 1, F2 = 1. Write a scipt that uses a for loop to compute the 10th element of the Fibbonacci sequence and assing it to the variable named f

EN (4)(p()) 5 (3c) Prove by induction that: Vn E N using your recursive definition from (2c) for the function defined below: p = n↔ 2n(n + 1) =: N → N Begin your work on this page and continue onto pages that follow, numbered as per instructions, as needed. 0 (i) BC 0 (ii) RCS You may discuss with anyone 319

is this correct? my number J is 00292366, i will also provide what s and b are from the different page i got it from, if incorrect, please fix it

please ignore the work already done for these as i am not sure they are correct.

4 - het B = { [´8 ], [ -5]} and C = { [4] [1]} Find the change of coordinates. matrix from ẞ to C and from C to B.