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Differential Equations

Differential Equations

Differential Equations: Change Your Euler True or False

1. The line below has slope -1.5.

Determine the value of the missing number. -> -3

2. Determine the indicated value.

-> 11

3. If f (x) = x2 + 3, use a tangent line to f at x = 1 to estimate f (.75). -> 4.5
4. The picture below shows the tangent line to f at x = 2:

Estimate f (2.1). -> 2.2

5. Let y = f (x) be a solution to the initial value problem

Use a tangent line to approximate f (1.5). -> 4.5

6. Let y = f (x) be a solution to the initial value problem

Use Euler's method with 2 steps to approximate f (3). -> 35.1

7. Let y = f (x) be a solution to the initial value problem

Euler's method with more than one step is used to approximate f (2). Which of the following numbers is most likely to be the value found by the approximation? -> 0

8. Let f (x) be a differentiable function defined for all real numbers, and let a be a real number. Which of the following statements is true? -> If f is concave up and decreasing then the tangent line to f at x = a lies under the graph of f.
9. If y(0) = 0 and , what is the error when Euler's method with 2 steps is used to approximate y(2)? -> 5
10. Let y = f (x) be a solution to the initial value problem

Euler's method produces -> an underestimate to the value f (1).


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