sketch sine integral curves. . T 101111111111 1111111111 11111111111111 1111111111111 111111111111 111111111111: 111111111111 111111111!* 111111111 ***...
Sketch the region enclosed by the curves and compute its area as an integral along the x- or y- axis. Sketch the region enclosed by the curves and compute its area as an integral along the e- or y-axis. (a) 1 = \y, r = 1 - \yl. (b) 1 = 2y, 2 + 1 = (y - 1)2 21 c) y = cos.r, y = cos 2.c, I=0,2 = 3
3. Sketch the region enclosed by the given curves and use a definite integral to calculate its exact area. y = 0,x=-1, y = 772 , x = 1
Sketch the region bounded by the curves y=e^x ,y=-x+2 and x=0, generate an integral of type-I and type-II, representing the volume of the enclosed region.
Sketch a direction field for the differential equation. Then use it to sketch three solution curves. y' = 7 + 7y y / / / / / / / / / /3 / // // IX х 1/-0.2 // 0.2 10.4 -0,4 -0.2 20,4 / / / / 0.2 0.4 / 1 1 +3 1 +3 y y 13 1 11 1 1 2 / / / / / / / / / / // х -0.4 -0.2 0.2 0.4...
. Sketch the curves below WITHOUT using a graphing device!!!! (a) ~ r(t) = (cost,1 + cos2 t,0), 0 ≤ t ≤ π/2. (b) ~ r(t) = 4cost~ i +~ j + 4sint~ k, 0 ≤ t ≤ 2π 2. Determine ~ T(t) and ~ N(t) for the following curves. (a) ~ r(t) = (cost,2sint,1), 0 ≤ t ≤ 2π (b) ~ r(t) = (3sint,3cost,t), 0 ≤ t ≤ 2π 3. Determine the curvature for the following curves. (a) ~...
makes) For each of the following direction field plots, write down a function f(ty) such that! the differential equation dy = f(t,y) could have this direction field. In each case, give reasons why you think your differential equation could have the direction field shown. + + + to TTTTTTT 1 1 1 1 - 111111111111 PTT TTT 1 1 1 1 1 1 1 1 1 1 1 1 1 UTILIITTI 1 1 1 1 1 1 1 1 III...
Consider the region R between the curves y = and y +7. (a) Sketch this region, making sure to find and label all points of intersection. (You are not required to simplify expressions for these if they end up being complicated. (b) Set up an integral for the area of this region using vertical rectangles. Do not evaluate the integral, just set it up. (C) (Harder! Do this problem last.) Set up an integral or integrals for the area of...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
2. (a) Sketch the region of integration and evaluate the double integral: T/4 pcos y rsin y dxdy Jo (b) Consider the line integral 1 = ((3y2 + 2mº cos x){ + (6xy – 31sin y)ī) · dr where C is the curve connecting the points (-1/2, 7) and (T1, 7/2) in the cy-plane. i. Show that this line integral is independent of the path. ii. Find the potential function (2, y) and use this to find the value of...
(4pts) Sketch the region S in R over which the integral is computed. 3 T/2 3 2π 0 0 1 (4pts) Sketch the region S in R over which the integral is computed. 3 T/2 3 2π 0 0 1