consider the subspace W of D given by W = span(e^2x, e^-2x) show that the differential operator D maps W into itself compute f(x) = cos(x) + 2xcos(x)
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consider the subspace W of D given by W = span(e^2x, e^-2x) show that the differential operator D maps W into itself compute f(x) = cos(x) + 2xcos(x)
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- VECTOR DIFFERENTIATION:If A = t(^2)i - tj + (2t+1)k and B = (2t-3) i + j - tk, obtain the following at t=1:a) d/dt(A dot B)b) d/dt(A x B)c) d/dt |A + B| d) d/dt (A x dB/dt)Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) = o²w'(X'X)-¹w.We can define an operator * : 2'(R?) → N'(R?) by defining +dx = dy and *dy = -dx, and extending linearly. If f : RR is a 0-form, show that af af d (d f): ) dx Ady.
- Let f(w)f(w)be a function of vector ww, i.e. f(w)=1/(1+e−wTx). Determine the first derivative and matrix of second derivatives of ffwith respect to w ?d/dt [sec^3(t)] compute the derivateLet vector r(t) = <5sin(t), 5cos(t), 2t^(3/2)> be the position function of an object.a. Find vector v(t) and vector a(t), the velocity and acceleration of the object.b. Find the speed of the object.c. Find the distance the object travels on the interval [0, 1]. Also find the average speed of theobject on this interval.