Actividad Carlos Alberto N M 3 Velazquez Camudio My 4xy Nx 4x = My 0 Nx 0 = = * * M(x,y) f(x,y) x2 c(y) 4y x - y = 2 7 7y + y 7y x + + xy2 3x - Y My c= = M(x,y) 3x = f(x,y) - = 2) 2yNx + - = dy c(y) 2y - - 2xy exacta es E 4y A 4x - c(y) 4x By - 2x = + + + E c = *lye No 4yx c(y) = 4y + M = = z + c 4Nx 4 = I xy3 - Fax)dx My 3x2y2 x + Nx = ydy 3x2y" = y N(x,y) xy f(x,y) +cx) - 2y4 4 4yx + = c * + 5 c(x) c(x) - + 1 - 3 /Fax - dr 3dx 3x = at = (1,d Fax) tanto 3 +C = - = c = tan'sx I 2y c=f(x,y) 5(x3y tanxx) xy3-tan'3x dx = dx = tan3x - = 0 = u = = = = 4 + + x2 My = + = = cy) + + = = * c(y) 3x &y xy c(y) (y c(y) + cy) 3y - 3 - = = x - y M(x,y) 2xy2 = f(x,y) x2y2 = = = E 3 My= * Nx=-senxcus senxcosy - N(x,y) cos xcus = = f(x,y) * cosxseny y y c(x) + = senx seny+ c(x) tanxreny - = = - v COS = Itanx dx (- fdr c(x) 4 +3 - = Af M(x,y) 4 = = 4 (y + = - 3 3 + dx x dx c 1 3 + - 3y - y - E c + + 1 1) + - y c(y) + + + + = 5 = - cly) y3 +y - sen = x 4 +d(y) 44 by - + = sen + + dt f(x,y) - c N+ 4 1 du = + seny-In1cus = - (n1cosx) (u)cos x) - = cosx My - = = du dx A 3 + - c + y y3 + + c + I 7 - - Actividad 4 Carlos dy udx ux y = (x - u)dx ~ x-d k((1-) ydx - (n)x ) 0 c + = x(* (n)x) + x(n/x) y + 5du M ku(u 1)dx -xudx 0 v((u )()dx xdv - = = - e V c) y((n)x) y 1) = = + E xc = y(n/x) ycE = x + (y x)dy (y x)dx vydx vdy ydv = = + vy(vdy ydv) (y -zvy)dy 0 y rigdy +vydv+y(1-2u)dy 0 (2 2 1)dy vydv 0 = vydv=-(v-1)"dy (da = - a c + c + = (n(y) - (x (x y)(nx y) - - y)(n)x y) - - - y = c + + x)dx + + - 1 y c - i)dx = = - + xdu + 0 = 0 = f(x)d = - = f(u)dx I iiten v =udv v 1dr zudv = = + dut/i, )I du ↓Inlulttanu=In1x) In1ul+ztan'u=2In1x) 2 + c + in1vl+1n1x4) 2tant c In 102+1) 1n1x) 2 tant = + c = + = + + + + 2tant In1.*) X Inly x) 2tanz + = xdu + xdv) + c = x)1 v)dx 0 ~ v)dx 0 x 2(u 1)d x(1 - (u 1)(udx x + InIv-ll-(v-1) (n(y) in1531-(*) = f(u)dx f(x)d lid=(n(a) dy udx ux = ( = + + a v 0 - + = + = (y x)dy (x y)dx + + - - = + x E + + 0 = 0 x =Yote - - r + - + = = + = + (du ) dx = 0 = = + = + + + xdr 0 = xudx x2d + ux y + + Velazquez Camudio dy vdx xdu (v vxdx x2(rdx xdu) xdu + = vx)dx x(udx xdu) - x(1 Alberto = ( => E x vdy ydv dx vy = + = y(udy + ydv) (vy - * ry.y) dy + + P(x) -yvdy -ydu y(v + r)dy k i v)dy ydv - 0 (25 (ny) ( (y c) + = = = - = y(a = = 4f(x) In = / Y *) + 1y = + X y * y(re!e - 3 y ↑ * X 4 z 24(x) u 4 e2dxex xu = 1 = xy4 2 + P(x) 1f(x) 0 = = (vd -dx In1xl = E (n(x) -> c - + 2 sts + y 3 a ex 4 4 v = y xy = + y - n x44) y - y = = + ↑ -Ya = - 3dx ((e 3) I - 3x.e - - = dv 3x v 3dx -3r y (x xe(udx uxex)dx - + e = - - xdu) 0 x(ve+1) dx-uxedx-xed x((ve+ 1) ve - xdx =>> - xed 0 = x - edu xdx = S *dx edu ed ~ = = x 2 e (n/x) => dx = e"- (n11) + c 1 ) = = 0 = = y 0 = x = ) e- (n/x) te ↑ 3 X - - 3x dx 3x I en - x -C 3 e 3x +C ) 6I -- éx I ~- * 3 * + ! - 3x 5 cex + + j cex + + t - > - > c = (n1x) e= x 3x edu = = = x vi = + e U - r-Judu edx x =x + = 3xdx = - = x = 3x - = u xdu = 3 y = e - dy wdx 4 = - E du - y + - ux - dX = = - x v + 4 dx M(x) e) c = dr = y1 = = = y) - = = y (11) ) (n(x) +3x/n(x) ( - = 3 = - = =In/x't c + 3E 4 =- - - = + - = y = U + + xn c + cx + y - = = = 0 *(1 -ydx Yudx xvd 0 (1 +y)dx xv2dr (x) y = a = 0 + * * + = + xud - = = x - = = + vx c 1 - = I) * * + dy udx xdu (x3 -3 3dx xvx2(udx~ xdu) y + I = + = + (a(xu) (dx y3)dx xydy = = = y => y = xy2dy (y3 x)dx (x3 y3 y! 2u = = 2 y= = sy=* * = = + + 0 y 1 - 4 = + 1 E - 23 19 = + dt P() 4 = - = - 1 y 2 j)(4 - 152. - f(t) - ) = 19 In A y= dy - = - -- M(t) e) + a = zu = - = 125) - - e(ty = = t = y -y - I y 1 y - = 1 + 1- 2 = - I =Iz => 2 =e(n1+) t = = (n) + 1y + ((+ v) (fa - t y = y! - + 1 = t + c) et = + (n) 1 = + = + e e =tE = - c +
