Module 18  Answers  
Lesson 1  
Answer 1  
18.1.1
Because , and , it appears that the exponent of x in the antiderivative is one greater than the exponent of the original function and that the antiderivative is divided by the value of its exponent. Predict that is . 

Answer 2  
18.1.2


Answer 3  
18.1.3
The TI89 results may appear to be different from your predictions, however they are algebraically equivalent to and , respectively. 

Answer 4  
18.1.4


Lesson 2  
Answer 1  
18.2.1
then


Answer 2  
18.2.2
The family of curves
is shown in a [4
, 4
] x [10, 10] window with 

Lesson 3  
Answer 1  
18.3.1


Answer 2  
18.3.2
The general solution is y = Ce^{x} .


Answer 3  
18.3.3
The solution to y' = 2x with y(2)=1 is y = x^{2} – 3. 

Answer 4  
18.3.4


Lesson 4  
Answer 1  
18.4.1
y(3) = 6 

Answer 2  
18.4.2


Answer 3  
18.4.3
Enter y1' = y1, not y1' = y, be sure to clear yi1, and use a [3, 3] x [5, 10] window.
Instead of parallel line segments in columns, line segments in rows are parallel. 

Self Test  
Answer 1  
The indefinite integral , displayed in a [2 , 2 ] x [5, 5] window, with C = 6, 4, 2, 0, 2, 4, 6. 

Answer 2  
y = (x^{3} – 3x^{2} + 6x – 6)e^{x} + C  
Answer 3  


Answer 4  
y(3) = 3 ln(3) 3.29584  
Answer 5  
[3, 3] x [2, 2] 

Answer 6  
[3, 3] x [1, 3] 

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