CK-12-Calculus

http://www.ck12.org Chapter 3. Applications of Derivatives

the differences between the actual and approximate values, we can enter into theY=menu the difference function
Y 3 =Y 1 −Y 2 as follows:

1. Go to theY=menu and place cursor on theY 3 line.


2. Press the following sequence of key strokes:[VARS] [FUNCTION][Y 1 ]. This will copy the functionY 1 onto
   theY 3 line of theY=menu.


3. Press [-] to enter the subtraction operation onto theY 3 line of theY=menu.


4. Repeat steps 1 - 2 and chooseY 2 to copyY 2 onto theY 3 line of theY=menu.
   Your screen should now appear as follows:

Now let’s setup the[TABLE]function so that we find the required accuracy.

1. Press2NDfollowed by[TBLSET]to access theTable Setupscreen.


2. Set the[TBLStart]value to 5 and 4 Tbl to 0.1.
   Your screen should now appear as follows:

Now we are ready to find the required accuracy.

Access the[TABLE]function, scroll through the table, and find thosexvalues that ensure|Y 3 |≤ 0 .01.

5. 3 ≤x≤ 6. 8

Non-Linear Approximations

It turns out that the linear approximations we have discussed are not the only approximations that we can derive

using derivatives. We can use non-linear functions to make approximations. These are calledTaylor Polynomials

and are defined as