Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing values of the approximate solution and the actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5. y' = − 6x²y, y(0) = 4; y(x) = 4e¯ - -2x3 ... Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (xn) 0.1 0.2 0.3 0.4 0.5

Q: Differentiate. x4 y: 3 — х3 y' У -

A:

Q: y = (r² + 4r) e"

A: given question is solved with the help of product rule of differentiation    i.e. (f.g)' = f*g'+…

Q: If z = 9x2 + y? and (x, y) changes from (1, 3) to (1.05, 2.9), compare the values of Az and dz. dz =…

A:

Q: Can you answer it and explain your steps

A:

Q: If QR = y- 10 and SU = y - 17, what is the value of y? %23 U %23

A:

Q: flx)=x =X-5 (x)= Find .f)

A: Here, the given function is: f(x)=x-5, g(x)=x2

Q: What is the process of differentiating these equations?

A: Given,          The equation is xx2+y232=E .

Q: Solve the ODE  y'=-2xy2

A: Solve the ODE  y'=-2xy2

Q: Evaluate f (; - 4) da

A: Given : ∫1x3-4dx

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)