cos'x dx sin 3x dx 2. an 45 sin cos'xdx 4 sin'xcos'x dr 44 sin'x cos'r dr 6. sin'xcosx dx 8. Jo sin'x cosx dx fa-sin 2x)' dx sin x + cos x dx 10. 9 f sin'z dx cos'x sin'x d 12. 11 sin'x Vcosx dx 14. 13. cot'r sin'x dx 16. cos'x tan'xdx 15 dx sin x dx 18. 17 1-sin x cos x tan'x dx 20. tanx dx 19 sec'x d sec'x dx 22. 21 tan'x secxdx...
Find dy/dx of the next relations Sol: y ylx 1 1-Cx C 2) 1+cx y' (1+cx1-cx a+bx ab 3) y= In Va-bx y's a2-b'x 4) y= atan (t); x = bcor (t) 6) x+2 7) y = 2v+ 45; donde v 52., W sec X 8)4x+3 8xy+e -e+ 8cos[tan(y)] = 0 arcsec (); x = elog2 (Int) 9) y 10) y sen[tan(x )] 11) y = cos[sen' (x)] cot + 4 12) y 13) y = [sec'(secx))P 14) y [Beae...
Solving Trig Equations class Activity 0 2 cos²x-√3 cosx=0 [0, 360) 6 Sinx + Cosx=1 [0, 21) (3 Sin (arctan 23-arccos 12) @ sin laoreet (5)
verify the following trigonometric identities. cos y 1-sın y 5, sec y + tany= cos x-sin x -cosx 1-tanx sinx cosx-l 7. sin20+cos 2 θ+ cot 2a 1+tan 2 θ 8.
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
3 cos(3x) I = dx 4+ sin- .1 I= 3cos(3x) -dx 4 + sin²(3x)
help with differential equations. having problems with the 2nd problem, 3rd, 6th, 7th, and the rest. I don't understand how to work the 2nd, 3rd, 6th, and the rest of the questions. Homework Problems for Handout Sheet 01 1. Show that y Ke' -2x+1 is a solution of V-y-2x-3, and then find K so that y Ke -2x+1 also satisfies y(0)-4 2. Show that y -Ke-2e +4xe is a solution of dy + y 8xe, and then find K so...
1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =
Question 11 Give the form of a particular solution of (4) – 16y-2 e 2x+3e" + cos2x) – 1 a) z-Axe* + Be **+Ccos(2x) + sin(2x) + E d) Axe 2+Be+Cx cos(2x) +Dx sin(2x) +B 3-Axe* +Be+3+ Cx cos(2x) +Dx sin(2x) + E 2=Axe 2+36-3x+cos(2x) + sin(2x) -Ae 2*+Be9*+ C'x cos(2x) + DX sin(2x) + E None of the above. e) f) Question 12 Give the form of a particular solution of J14) - 4 7 " +13 y" –...