6. Show that for a > 1/2, lim s W(1/s) s-+0 where the Iimit is taken in the mean square senuse.
Please answer the question and WRITE LEGIBLY - thanks 6. Show that for a > 1/2, s-0 where the limit is taken in the mean square sense. 6. Show that for a > 1/2, s-0 where the limit is taken in the mean square sense.
1. Suppose that lim x) = A, lim f(x) = B, 0) = C, where A, B, C are distinct real numbers. In each of the following, fill in the corresponding box by: • Expressing the limit in terms of A, B, C if it is possible to do so using the given information; • Writing DNE if it is possible to conclude that the limit does not exist using the given information; • Putting a X. otherwise. No explanation...
Using Python: Compute the Mean Square Error (MSE): ???=1?∑??=0(??−??)2 M S E = 1 n ∑ i = 0 n ( X i − Y i ) 2 . Where ?? X i and ?? Y i imply the ? i -th elements in ? X and ? Y , and ? n is the number of elements in ? X and ? Y (for example, create one-dimensional arrays ? X and ? Y with 5 elements).
6. Let si = 4 and sn +1 (sn +-) for n > 0. Prove lim n→oo sn exists and find limn-oo Sn. (Hint: First use induction to show sn 2 2 and the.show (sn) is decreasing)
Question 6: Show that, if a > 0, then lim (I.) = 0. (Hint: Mimic Example 5 on slide 12 Section 3.1).
solve d-f Find the limits and show your work. Use L'Hospital's Rule where appropriate. (a) lim-0 tan 3.0 2.2 1 (b) limu+0+ In(X) (c) limx→ In(x + 3) – In(3x + 2) (d) limz+ x sin(5) (e) lim.+ 22-45 4" +3: (f) limo (#2) (g) lim + (e+ + a)*
40 Show the following results. 1-e2 (e) lim(2+3-12)tan(/4) (24.3)-4/ 2 (a) lim -+0 isin(3r) エ→2 3 (f) lim(cos x)In | = 1 エ→0 1+ tanz1/sin z 1+ tanh r (b) lim = 1 -+0 nT nT (g) lim cos no0 +sin 6n+1 (c) lim (sin r)1/(2r-) - 1 エ→/2 = e 3n+1 2 + sin r 1 (h) lim 0. (d) lim エー→0 1 In (1 - V-1) - . 2 In(cos x) r+1+ 40 Show the following results. 1-e2...
4 Show, from the definition of mean square error that MSE(0) = V(0) + Bias(0)2. Justify all of your steps.
find the limits analytically, show all steps x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....
Question 3 (20 Points For each spectral density function defined below, determine the mean-square value of the random process. Show your work for full credit. ω) = else (2π)2 +25 (2mf+37(2)2+36 (s+0.5)(s-0.5) ω2 +25 w" +37a, 2 +36 TO (a)- Question 3 (20 Points For each spectral density function defined below, determine the mean-square value of the random process. Show your work for full credit. ω) = else (2π)2 +25 (2mf+37(2)2+36 (s+0.5)(s-0.5) ω2 +25 w" +37a, 2 +36 TO (a)-