To derive Euler’s method, we truncated the Taylor series expansion of yi+1 at the linear term. We could truncate at the quadratic term instead, giving the so-called Taylor method of order 2. This method approximates yi+1 byωi+1= ωi+ hf(ti,ωi) + h^2/2. df/dt| (ti,ωi)a. For the IVP y'(t)= y^2. e^-t, 0 ≤ t ≤ 1, y(0)= 1, Calculate df/dt. b. By hand, use both Euler's method and the Taylor method of order 2 to approximate y(1) with h=0.5

step-by-step explanation:

divide, then simplify your answer.

1. make -15.66 ÷   5.8 a fraction. then divide.

2. simplify.  

3. final answer.  

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: