Question

To estimate the value of a function y at =0.8x=0.8, with different step sizes ℎh.

Here's a possible corrected presentation based on the provided context:
(i) With step size ℎ=0.8h=0.8, estimate y(0.8): y(0.8)=
(ii) With step size ℎ=0.4h=0.4, estimate y(0.8): y(0.8)=
(iii) With step size ℎ=0.2h=0.2, estimate (0.8)y(0.8): y(0.8)=

Answer 1

To estimate the value of a function at x=0.8, we perform calculations using different step sizes. As the step size decreases, from h=0.8 to h=0.2, the estimates become more accurate. Exact results depend on the function being analyzed and require a calculator or computational methods.

Step-by-step explanation:

To estimate the value of a function y at x=0.8, we use approximate methods with given step sizes h. Since the problem statement provides a series of calculations leading to the estimation of the value for y, we can follow similar steps to provide estimates with different step sizes. The process might include techniques such as linear approximation, numerical methods, or iterative calculations like successive approximations.

Let's consider the step size h=0.8: we calculate y(0.8) using the given equations and values. Similarly, with h=0.4, we repeat the calculation process to find y(0.8) possibly by averaging or using a more accurate estimation method. Finally, for h=0.2 we again estimate y(0.8) using the refined step size which should yield an even more precise estimate.

It's important to use a calculator or computational tools for successive approximations and to refine the values for x and y based on the previously improved estimates. As the step size decreases, we generally expect our estimate of the function's value to become more accurate. Note that the specifics of the equations used are not detailed here, and calculation results would vary depending on the function being analyzed.