TL 0o Pn P, an 7-0 (a) Define T : Pl → R2 by T(ao + air) = (ao, (n). Note that T (2) L(P..R2). Fin(! (b) Define T1 R2P by T-(ao, aa. Note that TE L(R2.P). Find IT-1 TL 0o Pn P, an 7-0 (a) Define...
7. (25) Solve the following problems. (a) Find the limit (b) Find the interval of convergence of the following power series 0O TL Tl n-1 (c) Find the sum of the following power series and determine the largest set on which your formula is valid n= 1 (d) Let f(x) = cosa. Find T6(2), the Taylor polynomial of f at zo = 0 with degree 6 (e) Calculate the Maclaurin series for the following functio f(x) = In
7. (25)...
In problems (1) (2), Pn denotes the set of polynomials of degree at most n with real coef- ficients, on the interval [0, 1], and P denotes the set of all polynomials with real coefficients on the interval [0, 1]. That is, 0 These are normed vector spaces using the sup norm. (1) (a) Define D PP by Dp - p'. Note that DEL(P). Find ||D||. That is, find (b) Define D : P-> P by Dp p. Note that...
(1) X ∼ N(0, 1), define T = X^(−2) . Find the p.d.f. of T (2) X ∼ N(µ, σ^2 ). Define Y = X^2/σ^2. Find the p.d.f. of Y and the m.g.f. of Y
te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15 points by the normal direction toward the z-axis. Find the flux of the velocity field V 1and oriented (z2-ry2)i+(2.2y -yz2)j+ (y2z- 2r2)k across S Solution. To use Gauss Theorem, define C and C2 such that C1 {(a, y, z ) | a + y? < 2, z = 1} C2={(r,y,)| +y1.0} 11 TALK X W P S ww F6 & # 2 3 4...
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
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7) (20 pts) Let X(t)-At be a random process, such that A is N(0, 1). (b) Find the auto-correlation function of X, Rx(t1, t2) E[X(ti)X(t2)
(1 point) Let 1-11 ſi -1 31 A = 0 1 -1 and b=1-2 L-1 -2 0 [7] Define the linear transformation T:R* R* by T(T) = A. Find a vector a whose image under T is b. Is the vector i unique? choose choose unique Note: In order to get cred not unique all answers must be correct
Bus A Bus B R1 T1 line 1 20% 80% line 2 T2 R2 110 kV 11 kV Note TX impedance TX leakage reactance TX zero sequence impedance-TX positive Data 3 phase fault MVA Bus A 1152 MVA Single P-G level Bus A 8k T1 = T2 = 50MVA X1 0.006 RAk TX1 X2 0.0055 Rik TX2 Earthing resistance-R1-R2-2 ohm z+ sequence reactance 55j) ohm for both sequence impedance Source negative impedance -positive sequence impedance Source zero sequence impedance- purely...