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- ATAT 2i Find the egruation of the taingent: lme to tul Cur ve y= 4x-x* at the polnt (1,3).the f 17)= ez" tunction Show whether Ana lytic using Cauchy- Riemann equatiany isFind the lower bound for the radius of convergence for the followingdifferential equation: (x^2 + 4x+ 5)y′′+ (x^2 −4)y′+ x^2y= 0 about the point x0 = 5
- LaplaceTransform[Piecewise[{{1, 0 ≤ t < 2}, {4 - 4 t + t^2, t >= 2}}]The volume of the solid generated by revolving the region between the parabola x =y2+1 and the line x = 10 about the line x = 10 is = [° n[10- (v² +1)]°dy V= -3 None 10 ] "T[10-(y²+1)ľ°dy V= 10 S"n[10-(/x-1)]°dr V= ap,The path C is a line segment of length 13 in the plane starting at (4,5). For f(x,y)=5x+12y, consider∫C∇f⋅dr⃗ .(a) Where should the other end of the line segment C be placed to maximize the value of the integral? At x=____ and y=____ (b)What is the maximum value of the integral?
- Suppose a particle begins to move from the origin (t = 0) following the curve in space r(t)= (5sint, 5 cost, 121) Find the location of the particle on the curve at a distance 26T units along the curve from the origin in the direction of increasing t.A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at any time t and distance x from the origin where the velocity is u。 to become poo(vt — x). Prove that the velocity u (at time t and distance x from the origin) is given by v + (u。 – v) (vt) - o(vt - x)Please solve for the closed surface integral and then also solve the same integral using divergence theorem, thanks.
- Suppose that a turtle is moving along a straight line, and its displacement s(t) at any given time t (minutes) is given by the formula s(t) = (1 – VP + 3 + v3) units, 1 > 0. VP + 3 + V3 ) units, t> 0. (a) Compute the average velocity of the turtle on the interval [1, 2]. (b) Using a limit, compute the instantaneous velocity of the turtle at time t : 1 minute. (c) For the rest of the turtle's life it stays on the same straight line and moves according to the function s(t) given above. Where along the line does the turtle eventually end up in the long run?Find the area af the reabn eying behueen the x-oxis and the curve y= en(2x)-1 to the right the ene メーe x2 )(3+en (6) le b) (+en (6) le ) ((ren(ul)le dl (2+ en(6)le e)(++en(2)le ) (2+en(2)le 9)(2+ Cn (u)le/Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D