2. Let g(t)=e-2,[sin(6π) + 2 cos(3m)]. FindJa-2)g(t)dt. 3. Let g(1)=-2111(1)-11(1-2)|. Plot g(t) Using g(t) from problem 3, plot g| and g 4. i-2 5. Let g(t)=Πcos(2km. Is this an even or odd function. (Justify your answer) に!
Unanswered 0/2 pts Question 18 Let G(X) = Set (t? - sin(t?)) dt. Find G'(x). Correct Answer O evo [c2x – sin (e24)] sin (22) - 230 -e* [e2+ sin(e200)] 2xe 2.2 + cos(e230) 23 2* — sin (2) None of these
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE (1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
5. Laplace applications (1) 5*e**tcostdt = (2) ["sin 21 dt (3) [** :[e* sin Ardt Can you show steps.
let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].
Find the following integrals using integration by parts (IBP) (e) cos'(t)dt (f) S[In(t)]?dt (g) 83" 02 sin(20)de
Let F(x) = Sý sin*(0) dt. Evaluate the following limit . Let F(x) = $* sin?(t) dt. Evaluate the following limit. 2022
2. The nonlinear pendulum is governed by the equations du g sin e dt dt L Solve using a) forward Euler and b) backward Euler for L = 9m, At 0.1s, vo = 0.6m s-1 and 0, 0. Integrate for 25s and plot v as a function of t. Comment on your results. Note that if a scheme is implicit, you may have to iterate 4o convergence at each time step. Use your own judgement on how best to do...
Just (d) 1-26. Evaluate the following integrals. .10 (a) | cos 2nt δ(1-2) dt (b) | cos 2nt δ(1-2) dt (c) | cos 2nt δ(t-0.5) dt (d) (t 2)82) dt (e)S 2) dr Al
all parts -2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...