15. Suppose y= V5x+1 where x and y are functions of t. (a) If dv/dt =...
Suppose y = √(2x + 1), where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4 (b) If dy/dt = 4, find dx/dt when x = 40.
Assume that x and y are functions of t, and x and y are related by the equation y= 4x+3. (a) Given that dx/dt=1, find dy/dt when x=2. (b) Given that dy/dt=4, find dx/dt when x=3.
Consider three functions x(t), v(), and at), such that dx dt dv - alt) dt The function ) is given by )-. What is a(2)? (2)29 If x(0)29, what is x(3)? x(3)
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
1. -/5 POINTS LARCALC11 2.6.003. 0/2 Submissions Used Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = x (a) Find dy/dt, given x = 1 and dx/dt = 8. dy/dt = (b) Find dx/dt, given x = 64 and dy/dt = 7. dx/dt =
hw help Consider the equation exin(y)+5x +1=y? Find dy dx in terms of X and y. Evaluate dx at (x,y) = (0,1). Select the correct answer. -5 5 ООО 2 Suppose that 3 xy2 = x²y + y2 + 14. dy Use implicit differentiation to find an expression for in terms of both X and y. dx dy Now give the value of when x = 3 and y = 2 dx -36 13 3 0 24 41 о ....
Assume that x and y are both differentiable functions of t and are related by the equation 42 y= 22 +3 Find dy when 2 = 0, given dt de dt 2 when x = 0 Enter the exact answer. 11 dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
7. Assume x and y are functions of t. Evaluate dy/dt for each of the following. (a) y2 - 8x3 = -55, 5= -4,2 = 2, y = 3 (b) = 2, r = 4, y = 2 (e) cell = 2 - In 2 + In 2, 6,2 = 2, y = 0