# Differential Equations

# Differential Equations: Change Your Euler Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Differential Equations**Q. The line below has slope -1.5.

Determine the value of the missing number.

-3

8

14

There is insufficient information to answer this question.

Q. Determine the indicated value.

7

9

11

13

Q. If

*f*(*x*) =*x*^{2}+ 3, use a tangent line to*f*at*x*= 1 to estimate*f*(.75).5

1.5

3.5

4.5

Q. The picture below shows the tangent line to

*f*at*x*= 2: Estimate *f* (2.1).

2.2

2.3

3.2

3.3

Q. Let

*y*=*f*(*x*) be a solution to the initial value problem

Use a tangent line to approximate *f* (1.5).

3.5

4.5

Q. Let

*y*=*f*(*x*) be a solution to the initial value problem

Use Euler's method with 2 steps to approximate *f* (3).

13.5

15.3

31.5

35.1

Q. Let

*y*=*f*(*x*) be a solution to the initial value problemEuler'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

7

8

9

Q. 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*.If

*f*is concave up and decreasing then the tangent line to*f*at*x*= a lies over the graph of*f*.If

*f*is concave up and increasing then the tangent line to*f*at*x*= a lies over the graph of*f*.If

*f*is concave down except at*x*= a and*f*'(a) = 0 then the tangent line to*f*at*x*= a lies under the graph of*f*.Q. If

*y*(0) = 0 and , what is the error when Euler's method with 2 steps is used to approximate*y*(2)?3

5

6

8

Q. Let

*y*=*f*(*x*) be a solution to the initial value problemEuler's method produces

an overestimate to the value

*f*(1).an underestimate to the value

*f*(1).the exact value

*f*(1).a formula for the solution

*f*(*x*).