WMST 111 Lecture 5: societal norma

Find r (t) satisfying the given conditions. (Remember to use In |u| where appropriate.) r' (t) = t + 1i + t/t2 + 2 + 2/t k; r(3) = i + j + 2k Find the integral. [4/1 + t2i + t/2 + 2t2 j - 5/ 1 - t2 k] dt

Consider F and C below. F(x, y, z) = yze®i + exzj + xyexzk, C: r(t) = (t2 + 4)i + (t2-1)j + (t2-5)k, (a) Find a function f such that F = Vf rx, y, z) = 0 t 5 (b) Use part (a) to evaluate F dr along the given curve C

Consider F and C below. F(x, y)i 2y arctan(x) j 1 + X c: r(t) = t2 i + 3t j, 0 t 1 (a) Find a function f such that F = Vf f(x, y) = |y?arctan(x) 2 (b) Use part (a) to evaluate V. dr along the given curve C.