Find the value of the limit 2xy² lim (y) (0,0) x² + y²
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- Find the equation in xx and yy for the line tangent to the curve in polar coordinates r=5+cos(2θ)r=5+cos(2θ) at the value θ=π/3 What does y=(Yp)for ye) + 4y = 3cos2x ;is a. y = c, cos2x + c,sin2x b. y = x²(Acosx + Bsinx) y = x(Acosx + Bsinx) d. y = x(Acos2x +Bsin2x) %3DShow that r = cos(2pi) is symmetric about the y-axis.
- For a > 0, a lemniscate curve is the set of points P such that the product of the distances from P to (a, 0) and (−a, 0) is a2. Show that the equation of the lemniscate is (x2 + y2)2 = 2a2(x2 − y2) Then find the equation in polar coordinates. To obtain the simplest form of the equation, use the identity cos 2θ = cos2 θ − sin2 θ. Plot the lemniscate for a = 2 if you have a computer algebra system.Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please use Matlab to solve.Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation r = 2+ 3 sin 0. 2(5, 3n -1, ( 2, π) +>0 2 3 BIN RIN H