by arelength. Exercise 1/2 Consider the curve, alt) x(+)=(et, et vot). Reparametrize by arclength
a © lt (t) =<et, zee, 2t> a) compute the are arclength of the from tuoto tl. b) Reparemeterize the respect to *length. c) compute Ť, š, and B. F with d) Find formula for the curvature Evaluate it at t:1. e) Find the normal and osculating planes at t:1. f) Find the tangential and normal components of the acceleration t:1.
(b) Find the work done in moving a particle along the path x-cos y, z 0 from y-0 to y 2m, in the field F(x, y, z)-c" cosy i-xe® sínyi + 2xe2: cos y k. (10 Marks) EvaluatelFdA for surface S: x-z2,0 F(x, y, z)--Зугі + zer cosyj + 3xz2k. (c) y 2,-1 251and (7 Marks) (b) Find the work done in moving a particle along the path x-cos y, z 0 from y-0 to y 2m, in the field...
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 = ( y(t). Transform the above IVP to system of first order (a) Let u(t)y(t) and u2(t) IVP of u and u2. (b) Find y(t) by solving the system with h 0.1 (c) Compare the results to the actual solution y(t) = %et - te 2e t - 2. 5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 =...
Find the Laplace Transform (d) f(t) = te, 0<t<1, et, t > 1. l
The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minimizes the work done on the object by the force field. Please use the line work integral, and optimization
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T. (3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T.
Find the moment about the x-axis of a wire of constant density that lies along the curve y = /2x from x= 0 to x = 4 The moment is (Round to the nearest tenth as needed.) Find the moment about the x-axis of a wire of constant density that lies along the curve y = /2x from x= 0 to x = 4 The moment is (Round to the nearest tenth as needed.)
☺ (x²+2)y" +3 xy'-y = 0 Sol. -te altex *-* = ! ----**-**+1 = "h For each differential equation find two lineavly independent solutious about the ordinary point power series X=0
Find the exact length of the curve. x = et + et y = 5 - 2t, Osts 4