CK12 Calculus - Single Variable

In orderto view the differencesbetweenthe actualand approximatevalues,we can enterinto theY =menu
the differencefunctionY 3 =Y 1 Y 2 as follows:

1. Go to theY =menuand placecursoron theY 3 line.


2. Pressthe followingsequenceof key strokes:[VARS][FUNCTION][Y 1 ]. This will copythe functionY 1
   onto theY 3 line of theY =menu.


3. Press[-] to enterthe subtractionoperationonto theY 3 line of theY =menu.


4. Repeatsteps1–2 and chooseY 2 to copyY 2 onto theY 3 line of theY =menu.

Your screenshouldnow appearas follows:

Now let’s setuptheTABLEfunctionso that we find the requiredaccuracy.

1. Press2NDfollowedby [TBLSET]to accesstheTable Setupscreen.


2. Set theTBLStartvalueto 5 andΔ Tblto 0.1.
   Your screenshouldnow appearas follows:

Now we are readyto find the requiredaccuracy.

AccesstheTABLEfunction,scrollthroughthe table,and find those valuesthat ensureY 3. At
we see thatY 3 At we see thatY 3 Henceif

Non-LinearApproximations
It turnsout that the linearapproximationswe havediscussedare not the only approximationsthat we can
deriveusingderivatives.We can use non-linearfunctionsto makeapproximations.Theseare calledTaylor
Polynomialsand are definedas