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- 1) A y-intercept at y= 2) Roots at A and B, where A < B A = B= 3) Vertical asymptotes at C and D, where C < D C= D= 4) Horizontal asymptote at y =13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of -1 that occurs at x=11.Solve the d.e. dv/dt=9.8-0.196v and use desmos to sketch the family of curves with values of the arbitrary constants [-5,5], use integers only. From the family of curves, sketch the isoclines. Could you please show the sketch for isoclines? Thank you!
- Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the slotuion. (Enter your answer using interval notation.) (t-1)y''-3ty'+3y=sin t y(-8)=8 y'(-8)=11) The function, y =sin(5x-3t), represents a traveling wave with height y, position x andtime t.b) When t = 0, where is maximum x in the interval [0,2π]?c) When t = 1, where is the maximum in the interval [0,2π]?d) What is the speed and direction of this wave?Find the general solution using Reduction of Order: y''+y'=cos 3x
- Find the maximum and minimum values of the function ?(?)=10sin(?)cos(?)+11 on the interval [0,?/2] by comparing values at the critical points and endpoints.An electrical potential at a point (x,y) on the line segment extending from (0,3) to (2,0) is given by P=3x^2+2y^2. At what point on this segment is potential to maxima.A ball is thrown upward from the top of a 200-foot tall building with a velocity of 40 feet per second. Take the positive direction upward and the origin of the coordinate system at ground level. What is the initial value problem for the position, x(t), of the ball at time t?
- verify that the given function is a particular solu-tion to the specified nonhomogeneous equation. Find the general solu-tion and evaluate its arbitrary constants to find the unique solution satisfying the equation and the given initial conditions. y′′ - 2y′ + y = x^-1e^x, x >0, yp = xe^x ln x, y(1) = e, y′(1) = 0Assume that after months, butterflies’ populace in 1000 is calculated as: f(w)=12w+cos(16w)+n×100 Find maximum and minimum populace in 1st five months. Where n is your arid number for example if your arid number is 19-arid-1234 then n=1234Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4, 0). (Hint: Minimize the square of the distance as a function of t.)