Question

The table above gives selected values for the derivative of a function g on the interval —1 x < 2. If g(—l) = —2 and Euler's method with a step-size of 1.5 is used to approximate g(2), what is the resulting approximation?

Answer 1

(2.0, 2.5)

g(2) = 2.5

Explanation:

We can use Euler's Method by creating a table with 5 columns. The headers will be labeled, from left to right:

• (x, y)
• dy/dx
• Δx
• Δy
• (x + Δx, y + Δy)

We are given the starting point of (-1, -2). We can write this under the (x, y) column.

Check the given table for the dy/dx of the x-value we start with. We start with -1.0, so the chart says the change at this point is 2. Therefore, we can write 2 under the dy/dx column.

We are told the change in x is 1.5, so write 1.5 under Δx.

To calculate the change in y, multiply dy/dx times Δx.

• 2 * 1.5 = 3.0

Write 3.0 under the Δy column.

For the last column, take the previous columns and add them together for the new point. Use this new point to repeat the process until you find g(2).

I've attached an image of the chart that I drew to represent this process. Let me know if you have any questions!