5.3 - Euler'S Method Equation Worksheet (Page 5 of 6) in pdf

5.3 - Euler'S Method Equation Worksheet Page 5

WS 5.3: Euler’s Method

Calculus Maximus

9. AP 2002-5 (No Calculator)





Consider the differential equation:

(a) The slope field for the given differential equation is provided. Sketch the solution curve that passes

 





 .

through the point

0,1 and sketch the solution curve that passes through the point

0, 1

 

 .

(b) Let f be the function that satisfies the given differential equation with the initial condition

 

x 

Use Euler’s method, starting at

with a step size of 0.1 , to approximate

0.2

. Show the

work that leads to your answer.





x b

is a solution to the given differential equation. Justify your

answer.

(d) Let g be the function that satisfies the given differential equation with the initial condition

 





 . Does the graph of g have a local extremum at the point

0, 0 ? If so, is the point a local

maximum or a local minimum? Justify your answer.

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5.3 - Euler'S Method Equation Worksheet Page 5