Taylor and McLaurin Series Step by Step on the TiNspire CX – Calculus Made Easy

Finding Taylor Series and MacLaurin Series Step by Step using the TiNspire is as easy as pie:

Say you are asked to find the Taylor Series centered at a=0 up to degree n=3 (really a MacLaurin series as the center is at 0 )

So plug into Calculus Made Easy option 7 D as follows :

The derivatives are taken in order to compute the coefficients for each term up to degree 3.

The final answer is of degree 2 as the coefficient for the 3rd degree term is 0.

 

Additionally, other series topics such as interval of convergence and alternating series and Lagrange errors can be found as well using Calculus Made Easy at https://tinspireapps.com/?a=cme 

 

Finding Critical Points on the TiNspire CX CAS – using Calculus Made Easy

Finding Critical Points and also a relative & absolute Minimum or Maximum is easily done using the

Calculus Made Easy APP at www.TiNspireApps.com  . Simply select “Critical Points” in the Menu.

 

Here, you can either enter the given function f(x) in the top box or
enter its given derivative in the bottom box.  We enter f(x) in below’s example.

Then, the derivative f'(x) is computed

and simplified to a more compact expression:

finding its zeros yields the following x values of the critical points.

Since we entered a periodic trigonometric function f(x)
we obtain infinitely many critical points of the format
shown below. Note that n87 represents a constant which
is usually denoted as K in textbooks.

Besides finding critical points, Maximum and Minimum values
you will also be able to find saddle points and inflection points under this menu option.

 

 

TiNspire Integration via U-Substitution Solver – Step by Step – using Calculus Made Easy

Here are great news: Now Calculus Made Easy for the TiNspire CX CAS  offers you two different ways to

perform Integration using U-Substitution.

The first way is the fully automated: Just plug in your given function as seen below and steps and answer are displayed.

 

The second way requires your input on the choice of u. You may wonder what is

point if the fully automated version can do this already?  It is called LEARNING:

U Substitutions are not unique: Different choices of U may lead to the same solution.

Check out below’s example:

 

Check out another choice of U, it leads to the same solution.

Our Made Easy APPS aim at empowering students and this feature allows you guys to
learn about U-Substitution in a way you likely will not in your classroom. So enjoy this feature.

As usual, updates are free forever.

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Find the angle (Theta) between the two vectors using Vector Calculus Made Easy for the Ti-Nspire CX CAS

Say we have to..

Find the angle (Theta) between the two vectors

U= cos(pi/4)i + sin(pi/4)j

V= cos(pi/2)i + sin(pi/2)j

 

When entering these 2 vectors using option 1 6 in Vector Calculus Made Easy we will not use the i-j notation and instead use vector /matrix notation as  shown in this image . The angle is derived using arccos(AB/|A|*|B|) and given in radian format.

 

Note: We know that the vectors differ by an angle of pi/2-pi/4=pi/4 or .785  , which also equals 45 degrees.

Step by Step Engineering Mathematics using the Ti-NSpire CAS CX calculator program

Attention Engineers with a TI-Nspire CAS CX :

Engineering Mathematics has become much easier : this Steo by Step Ti-nspire app covers Math Topics for Engineers (i.e. FE Exam) such as Algebra, Complex Numbers, Conics, Trigonometry, Exponential and Logarithmic Functions, Calculus, Differential Equations with LaPlace Transforms, Statistics, Probability, Combinations & Permutations, Matrices and Vectors. Read Definitions & Theories.  For more details visit: http://www.tinspireapps.com/?a=EMME

 

Schrittweise Analysis mit dem TiNspire CX CAS

Mit der neuen Analysis Leicht Gemacht App bei www.TiNspireApps.de kann man nun Schritt fuer Schritt:

-Kurvendiskussion

-Stammfunktionen und Integrale

-Ableitungen

-Extremwerte

-DifferentialGleichungen loesen

-Grenzwerte finden

-Lhopital Regel

-Laplace Transformation

-Mehrfach Integrale

-Partielle Ableitungen

-Anwendungen

-Nullstellen (Newton)

-Reihen Konvergenz, Taylor Reihen, Folgen

-Potenzreihen

-Implizite Differentiation

-Vektoren

und vieles mehr!

Alles kann man spielerisch lernen und die Schritte fuer alle Loesungen anzeigen, sher handlich und immer dabei.

Super einfach zu benutzen und zu installieren.