MTHE 281 Lecture : Week 10-2

(1 pt) (St 1) i t sin t) j 5t4k, G Let F Find the vector derivative 5,tn (3)(4sin (t),tcos (t))20tA(3) (2) G. (3) H e 5t 4t cos(4t)j es k and H ri 1 t

2. For r E(oo, oo) define F by F(z) = | eta dt (a) Show that limo F(x) = oo. Hint: First show that er-1 for all t (b) Compute lim EF (c) Compute lim 0. F(x)

3. 2 points MarsVectorCalc6 7.1.011 My Notes Ask Your Teacher Evaluate the following path integrals f(x, y, z) as, under the following conditions. (Note that exp(u) = eu.) (a) fx, , z)-expV, and c: t (4, 2,t2),tE (0,1 (b) rx, y, z)-yz, and c: t→ (t, 2t, 3t), te [1,3]