![Consider: S x2-yds, C: r(t) = (e? 2, 1+e), te[0,2] Which one of the following regular integrals represents the above line](http://img.homeworklib.com/questions/29205370-9f74-11eb-b7af-81eabf4cf126.png?x-oss-process=image/resize,w_560)
![Question 8 10 point Consider: | <x?,v/dr, C: r(t) = (sint, cost), te[0,1] Which one of the following regular integrals repr](http://img.homeworklib.com/questions/29f4fca0-9f74-11eb-b044-b5202c2cf09d.png?x-oss-process=image/resize,w_560)
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Consider: S x2-yds, C: r(t) = (e"? 2, 1+e'), te[0,2] Which one of the following "regular"...
Consider: S (x + 2 x + y)z ds, C: r(t)= (2+, 1-37, 57 +5), te[0,1]...
Consider: S (x + 2 x + y)z ds, C: r(t)= (2+, 1-37, 57 +5), te[0,1] Which one of the following "regular" integrals represents the above line integral. -5/38 | 2+31 – Ide a. Ob och 2-33+ 101 -551-pat Od -s/38 1-10
Consider: 5x2-y’ds, C:r(t)=<2t, – 1), te[0,11 Which one of the following "regular" integrals represents the above...
Consider: 5x2-y’ds, C:r(t)=<2t, – 1), te[0,11 Which one of the following "regular" integrals represents the above line integral. 312dt 1 oors ! *52-2 + 14t V5S 3+2+2t - 1dt Ос. 1 d. f 31² + 28-1dt 1 -15% 312 +2t - 1dt
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
soi-Ja x(rprr) a r, where x(r) is continuous at t-o.anda <0< β. 3.13 Show that (a) (t - T)s-T)0, (c) cos(1)s(...
soi-Ja x(rprr) a r, where x(r) is continuous at t-o.anda <0< β. 3.13 Show that (a) (t - T)s-T)0, (c) cos(1)s(t + π/2),: 0, 3.14 Evaluate the following definite integrals: (a) sin(r)s)dr, (b) o sinoo)dt (c) sin(r)8(r)a(t-2) dr, τ cos(r/2)δ(r-x) dr.
soi-Ja x(rprr) a r, where x(r) is continuous at t-o.anda
Suppose C is a curve parametrized by r(t)=<cost,sint,1> and S is the portion of z=x^2+y^2 enclosed...
Suppose C is a curve parametrized by r(t)=<cost,sint,1>
and S is the portion of z=x^2+y^2 enclosed by C, located in the
vector field F=<z,-x,y>.
25. Suppose C is the curve parametrized by F(t) = (cost, sint, 1) and S is the portion of z = x2 + y2 enclosed by C, located in the vector field F = (2, -,y). Verify Stokes' theorem. That is, find show they are, in fact, the same. fe dr and SIC (curl ) ñds...
(e) /(z) = and γ is parametrized by r(t), 0 z + t 1, and satisfies Imr(t)> 0, r(0) -4 + i, and γ(...
Problem 4.9
(e) /(z) = and γ is parametrized by r(t), 0 z + t 1, and satisfies Imr(t)> 0, r(0) -4 + i, and γ(1) 6 + 2i (f) f(s) sin(z) and γ is some piecewise smooth path from 1 to π. 4.2 and the fact that the length of γ does not change under 4.9. Prove Proposi reparametrization. (Hint: Assume γ, σ, and τ are smooth. Start with the definition off, f, apply the chain rule to σ...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j + (cy + eylz cos.) k. (a) Show that F is a gradient vector field by finding a function o such that F = Vº. (b) Show that F is conservative by showing for any loop C, which is a(t) for te (a, b) satisfying a(a) = a(6), ff.dr = $. 14. dr = 0. Hint: the explicit o from (a) is not needed....
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial in...
Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial initial current going through the inductor is i(0-) -0 A and its first derivative is i(0)-1A/s. We are interested in the evolution of the current i(t). ve(t) i(t) The corresponding input-output relationship is i(r)dr Ug(t) + Li'(t) + Ri(t)-r(t) with t e(t)-ve(0) + (0) Which physical quantity is the input of the system? Explain. (ü) Which...
Consider the following fictitious mechanism: Step 1. R+S T, (fast, reversible) Step 2. T +U -...
Consider the following fictitious mechanism: Step 1. R+S T, (fast, reversible) Step 2. T +U - W + S, slow Which is the rate law for the reaction? Select one: o a. rate = k[R][U][S] O b. rate = k[S] o c. rate = k[T] 0 d. rate = k[R][S] o e. rate = k[W][S]
Consider: S (x + 2 x + y)z ds, C: r(t)= (2+, 1-37, 57 +5), te[0,1] Which one of the following "regular" integrals represents the above line integral. -5/38 | 2+31 – Ide a. Ob och 2-33+ 101 -551-pat Od -s/38 1-10
Consider: 5x2-y’ds, C:r(t)=<2t, – 1), te[0,11 Which one of the following "regular" integrals represents the above line integral. 312dt 1 oors ! *52-2 + 14t V5S 3+2+2t - 1dt Ос. 1 d. f 31² + 28-1dt 1 -15% 312 +2t - 1dt
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
soi-Ja x(rprr) a r, where x(r) is continuous at t-o.anda <0< β. 3.13 Show that (a) (t - T)s-T)0, (c) cos(1)s(t + π/2),: 0, 3.14 Evaluate the following definite integrals: (a) sin(r)s)dr, (b) o sinoo)dt (c) sin(r)8(r)a(t-2) dr, τ cos(r/2)δ(r-x) dr.
soi-Ja x(rprr) a r, where x(r) is continuous at t-o.anda
Suppose C is a curve parametrized by r(t)=<cost,sint,1>
and S is the portion of z=x^2+y^2 enclosed by C, located in the
vector field F=<z,-x,y>.
25. Suppose C is the curve parametrized by F(t) = (cost, sint, 1) and S is the portion of z = x2 + y2 enclosed by C, located in the vector field F = (2, -,y). Verify Stokes' theorem. That is, find show they are, in fact, the same. fe dr and SIC (curl ) ñds...
Problem 4.9
(e) /(z) = and γ is parametrized by r(t), 0 z + t 1, and satisfies Imr(t)> 0, r(0) -4 + i, and γ(1) 6 + 2i (f) f(s) sin(z) and γ is some piecewise smooth path from 1 to π. 4.2 and the fact that the length of γ does not change under 4.9. Prove Proposi reparametrization. (Hint: Assume γ, σ, and τ are smooth. Start with the definition off, f, apply the chain rule to σ...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j + (cy + eylz cos.) k. (a) Show that F is a gradient vector field by finding a function o such that F = Vº. (b) Show that F is conservative by showing for any loop C, which is a(t) for te (a, b) satisfying a(a) = a(6), ff.dr = $. 14. dr = 0. Hint: the explicit o from (a) is not needed....
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
Consider the following circuit , where the voltage v(t) is imposed for t 2 0, R 4 Ω, L-1H and C 1/4F. The initial initial current going through the inductor is i(0-) -0 A and its first derivative is i(0)-1A/s. We are interested in the evolution of the current i(t). ve(t) i(t) The corresponding input-output relationship is i(r)dr Ug(t) + Li'(t) + Ri(t)-r(t) with t e(t)-ve(0) + (0) Which physical quantity is the input of the system? Explain. (ü) Which...
Consider the following fictitious mechanism: Step 1. R+S T, (fast, reversible) Step 2. T +U - W + S, slow Which is the rate law for the reaction? Select one: o a. rate = k[R][U][S] O b. rate = k[S] o c. rate = k[T] 0 d. rate = k[R][S] o e. rate = k[W][S]
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