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# Accuracy and Usefulness of Euler's Method Exercises

### Example 1

Let y = f (x) be a solution to the IVP

What is the error when Euler's method is used to estimate f (2) with a step size of 0.5? With a step size of 0.25?

### Example 2

If f is concave up around x = a, is the tangent line to f at a above or below the graph of f? What about if f is concave down?

### Example 3

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (2)?

### Example 4

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (3.5)?

### Example 5

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (1)?

### Example 6

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (2)?

### Example 7

Let y = f (x) be a solution to the IVP

Does Euler's method produce an over- or under-estimate for the value of f (5.9)?