Question

consider the initial value problem in this question we will use a spreadsheet to approximate the value . the picture below shows a spreadsheet being used to implement a linear approximation scheme (ie. euler's method) with initial value and a step size of to make such an approximation in steps. a downwards arrow indicates that the contents from the cell above will be dragged down. column b holds values of ; column a holds approximations of ; and column c holds approximations of . a b c 1 3 0 ? 2 ? ? 3 4 5 6 7 8 9 10 (a) which entry should go in cell c1? a.

Answer 1

Cell C1 in the spreadsheet for Euler's method should contain the derivative of the function at the initial point based on the initial value from cell A1 and the step size from cell B1.

Step-by-step explanation:

For the initial value problem described, Euler's method is used to approximate the value of a function based on its derivative and a starting point. In this spreadsheet scenario, cell C1 should contain the derivative of the function at the initial point, which is based on the known variable in cell A1. Cell B1, which holds the value of the step size, is also taken into account. By identifying the initial value and using the step size from cell B1, we should calculate the change in the function's value. This change is then used to find the next approximation in cell A2.

To solve for cell C1, you need to use the formula that represents the derivative of the function you are approximating. The exact formula would depend on the function provided in the problem statement, but typically it would incorporate the initial value from cell A1 and possibly other constants or variables if they are given. The result of this calculation is entered in cell C1 as the starting derivative value for Euler's method.