9.(NC) The table below shows empirically obtained values of xand the continuous functionfx( )If the Trapezoidal rule is used with Δx=0.5, what is the approximate value of fx13∫dx?x11.522.53fx( ). ( )45134A()6.5 B()7 C()13 D()26

##### We have textbook solutions for you!

**The document you are viewing contains questions related to this textbook.**

**The document you are viewing contains questions related to this textbook.**

Expert Verified

4.10 Slope Field 1.Shown here is the slope field for which differential equation?

2

4

2

22. Shown here is the slope field for which differential equation?

1

2

1

1

3. Shown here is the slope field for which differential equation?

4

4

5

2for which differential equation?2dyyydxxdyxdxxdyydxdyydxxdyydxx−=22

322eyxyxyxyx=== −==()()6. The slope field for a differential equationis shown here. What statement is true about a. I only xxxdyfxdxy xyy xyy xyy x=5. Shown here is the slope field for the differential equation.What is the solution to thisdifferential equation?

5

yeyxyxyxyx=== −==()()6. The slope field for a differential equationis shown here. What statement is true about a. I only xxxdyfxdxy xyy xyy xyy x=( )()( )()( )()I. If 02 then limII. If 202 then limIII. If 02 then lim→∞→∞>≈ −−<<≈ −< −≈ −b. II only c. I and II d. II and III e. None of the above

?

2

2

2

→∞

7. The slope field for the diffential equation () is shown below for -5x5 and -5y5. Which of the following statements is true for all possible solutions of the differential equation?I. For dyf xdx=<<<<x0, all solution functions are decreasing.II. For x0, all solution functions are increasing.III. All solution functions level off near the y-axis.

4.11 Euler’s Method You may check with calculator, but to find the answer, you cannot use the calculator.

02. What is the approximation for if Euler's Method is used, with a step size of 1?2

2. The solution of the differential equation contains the point (1,2). Using Euler's method with 0.3 what is the approximate value of y when 1.3?

D

3. Let be the solution to the differential equation /. The point (3,2) is on the graph of the solution to this differential equation. What is the approximation for (5) if Euler's method yfxdydxxyf==−is used, starting at 3 with a step size of 0.5?

E) 4

()()6. Let be the solution to the differential equation. The point 5,1is on the graph of the solution to this differential equation. What is the approximation for 5.6 if Euler's Method is usedyfxyxdxf=−d, starting at 5 with a step sized of 0.3?

()( )24. Let f be the function whose graph goes through the point (0,1), and whose derivative is given by1. What is the approximation for 1if Euler's Method is used, starting at 21with a stxefxfxx+′==+ep size of 0.5?099A) 0 B) 1 C) 2 D) E) 24ee++