Find a map s: R → R şuch that S(3) s(0) - 1, s(2) + 4s' - 4s = 0, s'(0) −1, - - = s'ʼ(0) = 1.

Q3. Using u = 1-2u u²e-u-u 2u-1 A) B) ²e+u 1-2u C) u²e-u-u D) E) X 1+2u u²e-u-u the ODE dyy²ex/y = x²-2xy du = xdx dx du = 1-2u u²e-¹+2u²-u X du =– xdx du = du =- dx X dx X dx becomes

1) Given the mapping F(x,y,z)3(3e",xz sin 2y ,xy), v=(2,2,-1), using the definition, then the corollary (the Jacobian), compute the tangent map F., (v) at the point P-(-1,2,-2) ôf 2) Show that U:[S]- in R',where U, is the unit natural frame ôx, field and / is a real valued function on R'.

9 c and d