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Question 10- Consider the function: f(1) = etan 2 + In(r+ 2r - 1) + sin...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
QUESTION 4 (4.1) Consider the variational problem with Lagrangan function 2r Sin t and endpont conditions z(0) 0, z(*/2) = 1 (a) Find the smooth extremal of the gven vanational problem (7) (6) (b) Compare the value of the fundamental integral dt along an extremal between those two endpoints wnth the value along the curve z 1-cost through the two points Hint: You may use integration by parts and also remember that cost-(1+cos 2t), ant (1-cos 2t) and sin 2t...
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...
Verify the following using MATLAB
2) (a) Consider the following function f(t)=e"" sinwt u (t (1) .... Write the formula for Laplace transform. L[f)]=F(6) F(6))e"d Where f(t is the function in time domain. F(s) is the function in frequency domain Apply Laplace transform to equation 1. Le sin cot u()]F(s) Consider, f() sin wtu(t). From the frequency shifting theorem, L(e"f()F(s+a) (2) Apply Laplace transform to f(t). F,(s)sin ot u (t)e" "dt Define the step function, u(t u(t)= 1 fort >0...
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where I (rrr2dr-| , and ?, ? are the azimuth and polar angles, respectively. (i) Rewrite the wave function in terms of the appropriate spherical harmonics. (4 marks) (ii) What are the possible measurement results of the z-component L, of the angular momentum of the electron in this state? (6 marks) (iii) Calculate the probability of obtaining each of the possible results in part (i)....
Consider the differential equation: (7y sin(xy) + 2 sec x) dx = (2 lny – 4x sin(xy))dy Note: Do not use square brackets in your response, use normal parantheses if you have to, i.e "0" Then aM ду and ƏN ax Is this equation exact? Yes No Consider the differential equation: sin(x)dx + 5y cos(x)dy = 0 Which of the following can be an integrating factor to make the equation exact? Select all that apply. On=e-54 On=tan(x) Ju=e-542/2 On =...
Find sin , cos , and tan - O A. sino= _ . cosO=- , tan 0= - 13 O B. sino= - ], COSO = 3, tan o=1/3 o c. sino=- , coso - ., tan og OD. sino - 13. COSO = 1, tan 0=13 Find the exact value of sin 510º. O B. v O A. OC. O D. Find the exact value of tan 111. OA OB. Z OD. 13 OC. 2 Suppose that there is...
Establish the identity. 1 - sin e 1+ sin e = (sec - tan e) Starting with the right side, which shows the key steps in establishing the identity? 1 + sin e 1 1 - sin 0 OA. (sec 0 - tan 9)2 = sec? -tan?= (1 - sin 02 1- sin 1 - sine ОВ. 2 sin 0 sine (1 - sin oy? (sec - tan )2 = cos? e cos2 e O c. 1 - sin (1...