One of the following is symmetric about the origin: A) f(x) = x³ + |x). B) f(x) = x cos(x). %3D %3D C) f(x) = x5 + 1. D) f(x) = x3 +x². E) f(x) = sec(x). %3D

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Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

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Q: 2. Differentiate y os=1(-2x³ – 3)³ = cOs

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A: Our Objective is to find the derivative.

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Q: 1.) Evaluate In 2 e*2arctan e* J (1+ e2x) sec(2arctan e*)' А.) -dx. ežr(1 – e*r)- (arcsin e 2x) cos²…

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Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

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Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

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Q: A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og ys x*

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Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

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Q: 19. For all positive angles less than 360°, if csc(2x +30°) = cos(3y- 15°), the %3D sum of x and y…

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Q: In Exercises 1–18, find dy/dx. cos x 1 + sin x 12. y = cos x 14. у — cos x

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Q: Example B Consider the inhomogeneous equation Yk+1 – 2yk coS Ø + Yk-1 = Rx, sin ø # 0, %3D

A: Given           yk+1-2ykcosϕ+yk-1=Rk  ,  sinϕ ≠0       ... (1) where ϕ is constant and Rk is…

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