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(c) e²™ ( − 3sin(3x) + 2 cos(3x)). (d) e²x ( — 2sin(3x) + 3 cos(3x). (e) e²x ( − sin(3x) + cos(3x)). 2. Page 3. MATH 1241 FINAL EXAM. PART I. SPRING 2014. 5 ... sa sinu du= -cosu+ (= - cos/√x) + C. U=3x du=3dx. 4S JX. U=√x dur 24/7 dx. 5. S cos(3x) dx. { sinu +(= {} sn13x |. 6. $ et dz. S =}{} cosu dy = = sinu + C =. Nov 21, 2023 ... ... e − 2 x cos ⁡ 3 x {\displaystyle \displaystyle -6M{{e}^{-2x}}\sin 3x+(-8M+6N){{e}^{-2x}}\cos 3x-10Mx{{e}^{-2x}}\cos 3x=2{{e}^{-2x}}\cos 3x}. Dec 16, 2014 ... 3x. 3x cos 3x. 1x 5. (b) (4 marks) lim q14= +0--2. ما. Page 10. 201-NYA-05 Calculus 1 Science. Final Exam A- Page 10 of 15. December 16th 2014. Yp = -9 A Cos 3x-9B Sin 3x. Plug into ODE: (-9A (os 3x-98 Sin 3x)+4(-3A Sin 3x + 3B Cos3x). + 4 CA Cos 3x + B Sin 3x). = [-5A ]. T-5. +12B Cos 3x + -12A-5B ... 4. Trial and error. Ex 1. = tan 3x. S dx cos 3x. =S. ← trigonometric substition sin 3x | cos 3x cos 3x. 5213x. Cosx dx u = Ja dx. (1-cos²x) sanx dx. 1053X. 1-42. Dec 15, 2016 ... ... integrals: a. J 1+x-3 - ~ +e= +cos(3x) +1['2 b. JxV x2 +1 dx c. JxJX+I dx. 1~x cos(x) - sin x d e. 2 x. ,.,. X. 4". Page 4. 4. Sketch the curve ... ... cos(3x). Figure 5 shows the zero level set of visibility function for an observer at (0.02, 0.02, f (0.02, 0.02)) where f = cos(5 x 2 + y 2 π) − 4(x 2 + y ... cos (ax+b) dx e.g. √(3x=2x) cos (3x) dx. Special Cases. x²=2x+3 sinx) (sinx) ... +3=x -3x. S. 1+x². (4-1) dx = √(u. и du dx. =2x = d₂ = du. 2x du. = 24. Sudu. (cos(x) + isin(x)). 3. = cos(3x) + isin(3x). By comparing coefficients, we have cos(3x) = cos. 3. (x) − 3 sin. 2. (x) cos(x) and sin(3x) = 3 sin(x) cos. 2.