From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Differential Equations

Differential Equations

Differential Equations: Change Your Euler Quiz

Think you’ve got your head wrapped around Differential Equations? Put your knowledge to the test. Good luck — the Stickman is counting on you!
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) = x2 + 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 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
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 problem

Euler'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).
Advertisement