Use graphs to find groups of expressions that appear to be identically equal. (a) 2cost + sin t +1 (b) cos (c) cos (21) (d) 1 - 2sin? (e) 2 sint cost (f) cos't - sint (9) sin (21) (h) sin (31) (i) —2sin’t + sin t +3 (i) sin (21) cos + + cos (2t) sin 1-sint 1 + cos (21) (k) (1) sint 2 (m) ( cas 1-1) 1 - cost Select each group of identical expressions. x...
2 + 3s +2 (2s + 9)e-38 20. If F(s) = ? (S-2)(2+4)52+45 + 13 then L-'[F(s) = 2e2+ i sin 2x, OSI<3 (a) f(x) = { 2e2(-3) cos 3.- 3) + 2(1-3) sin 3(2x - 3), 1 3 2e22 + 3 cos 21, 0<x<3 2e2+ + 3 cos 2x + 2e-22 cos 3.0 + e -2- sin 3r, r>3 2e2+ + 2 sin 21, 05x<3 2e2+ sin 2r +2e-2(-3) cos 3(x - 3) + e -2(2-3) sin 3(-3), 1...
Find the derivatives of the following functions. a) f(x) = sin(x²) b) g(x) = ln(cos(x)) c) h(z) – In(1002? + 47x)? d) k(z) = resin(2)
(a) Are the functions h(a) 1,(z) cos (2z) and fs(z) sin(x) linearly independent? (b) How about the functions f(a)1, Ja(ar)sin (a) and fs(a)sin ()? Why or why Why or why not? not? (Hint: Plug in 3 different values of z to get a linear system for the coefficients in the definition of linear independence.)
Question 12 11. Show that if F is continuous on Rn and F(X + Y) = F(X) + F(Y) for all X : in R", then A is linear. HINT: The rational numbers are dense in the reals. 12. Find F and JF. Then find an affine transformation G such that F(X)-G(Y) lim =0. T x2+y+2z (a) F(x, y,z)coxy. Xo- (1,-1,0) e*yz ex cos y (b) Fe*sin y 1, xo=(0, π/2) 13. Find F. g1 (x) 11. Show that if...
Questions 10 and 16 ((State the max and min values) SKILLS 5–18 - Graphing Sine and Cosine Functions Graph the function. 5. f(x) = 2 + sin x 6. f(x) = -2 + cos x e. 7. f(x) = -sin x 8. f(x) = 2 – cos x 9. f(x) = –2 + sin x 10. f(x) = -1 + cos x 2. 11. g(x) = 3 cos x 12. g(x) = 2 sin x 13. g(x) = – į...
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d) f(x) = (1 + x)'(1 - x)2 1 e) f(1) = 2009 1672 f). f() = ln(sec 0 + tan ) B): S(21) = 1n () h) y = (In(ax)? g(x) = ln(2.3 - 3x + 2) i) c) f(x) = sina
9 and 11 please 2-11 CAUCHY-RIEMANN EQUATIONS Are the following functions analytic? Use (1) or (7). 2. f(z) = izz 3. f(z) = e -2,0 (cos 2y – i sin 2y) 4. f(x) = e« (cos y – i sin y) 5. f(z) = Re (z?) – i Im (32) 6. f(x) = 1/(z – 25) 7. f(x) = i/28 8. f(z) = Arg 2TZ 9. f(z) = 3772/(23 + 4722) 10. f(x) = ln [z] + i Arg z...
Please help me solve this, thanks! Give the Laplace transform for f (x)=4 x sin(3x) – 2x cos(4x) b ) = 245 __ 2(32 – 16) (2+0) (2 + 16) c) F(S) =_24 5 _ _ 2 (2+16) (32+0) (52-16) 165 F18) - 4 (32-9)_ _165 (52+0)2 (+16) e) 4 (3² – g) F(s) = ? (32+)2 85 62 +16) f) None of the above. Find [e sinh(4x) + 2 e*cosh( 2x)] ੩੦ -ਜਗਤ ਜੈ। b) ੦ - - -...
f(x) = 2x+4, g(x)=2x? + + 1; Find (gof)(1). O A. 10 OB. 19 O C. 73 OD. 16