7.2. Conditions for Applying the Method

Try these first

1. 1.

   What form of functions can you use the method of undetermined coefficients on?

   Hint

   Think of common mathematical functions.

2. 2.

   Give an example of a suitable polynomial function.

   Hint

   Look for a function made up entirely of powers of x.

3. 3.

   Which of the following is a suitable function for the method of undetermined coefficients?

   • A. ln(x)
   • B. x^2
   • C. tan(x)

   Hint

   Recall the types of functions outlined in the section.

4. 4.

   True or False: The method of undetermined coefficients can be applied to the function f(x) = 2*sin(3x).

   • True
   • False

   Hint

   Remember if sine and cosine functions are applicable.

5. 5.

   Is the function f(x) = e^x + sin(x) suitable for the method? Justify your answer.

   Hint

   Think about how derivatives maintain their function types.

6. 6.

   Create a function involving a combination of a polynomial and an exponential that can be used in this method, and explain its suitability.

   Hint

   Consider whether derivatives shift functions out of the usable types.