Numerical methods problems 1, 2 and 3 1. Find the area of the region bounded by f(x)-25-x2 , g(x)-V36-x2 . x=2, and (a) right Riemann sum with 8 segments. (b) midpoint rule with 8 segments (e) Sim...
1. Find the area of the region bounded by f(x)-25-x2 , g(x)-V36-x2 . x=2, and (a) right Riemann sum with 8 segments. (b) midpoint rule with 8 segments (e) Simpson's rule with 8 segments. Determine the average of the function f(x)=2x sinyx on the interval [1.8,3.4] using Romberg rule for 1, 2, 4 and 8 segments. 2, A new fuel for recreational boats being developed at the local university was tested at an area pond by a team of engineers. Their interest is to document the environmental impact of the fuel how quickly does the slick spread? The table below shows the video camera record of the radius of the wave generated by a drop of the fuel that fell into the pond Time, t (s 3. 2.5 3.5 3.0 2.0 1.0 Radius, R (m) o 0667 1.886 2.6353.464 4.365 Use second order polynomial interpolation to compute the rate at which the radius of the drop was changing at t = 3.2 seconds. Use the forward divided difference approximation to compute the rate at which the area of (a) (b) the drop was changing at 1 2.4 seconds.
1. Find the area of the region bounded by f(x)-25-x2 , g(x)-V36-x2 . x=2, and (a) right Riemann sum with 8 segments. (b) midpoint rule with 8 segments (e) Simpson's rule with 8 segments. Determine the average of the function f(x)=2x sinyx on the interval [1.8,3.4] using Romberg rule for 1, 2, 4 and 8 segments. 2, A new fuel for recreational boats being developed at the local university was tested at an area pond by a team of engineers. Their interest is to document the environmental impact of the fuel how quickly does the slick spread? The table below shows the video camera record of the radius of the wave generated by a drop of the fuel that fell into the pond Time, t (s 3. 2.5 3.5 3.0 2.0 1.0 Radius, R (m) o 0667 1.886 2.6353.464 4.365 Use second order polynomial interpolation to compute the rate at which the radius of the drop was changing at t = 3.2 seconds. Use the forward divided difference approximation to compute the rate at which the area of (a) (b) the drop was changing at 1 2.4 seconds.