Honors AP Calculus / Mr. Hansen

Name: ____________________

12/17/2009

 

 

Sleep Week Test through Chapter 7

 

Neatness counts!

 

 

1.

Consider the equation .

(a)

How would you assign the given equation a place in your cognitive map? (Use words such as “order” and “separable” or “non-separable” in your answer.)

 

 

 

 

 

 

(b)

Sketch the slope field for the lattice points in the region [−2, 2]  [−2, 2].

 

 

 

 

 

(c)

Given: When x = −0.75, y = 0. What name do we give to the point (−0.75, 0)?

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(d)

Use the information given in (c), along with Euler’s method using a step size of 0.25, to estimate y when x = 0. Show adequate work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(e)

Should your estimate in (d), if calculated correctly, be greater than or less than the true value for y when x = 0? Use the value of  to justify your answer. Note that you can answer (e) even if you did not get a correct answer to (d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.

Given: , and y = 2.2 when x = 0.45.

 

 

 

Solve, and circle your solution. Then use your solution to estimate y(3).
         

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.

Prove . What are the restrictions on x and b? _________________

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.

Simplify . What conditions are required for c?