Category: TI 84 Plus techniques

Quick Maclaurin’s series expansion using GC

In Maclaurin’s series expansion, where up to f”(0) need to be evaluated, can be done quickly using the GC.

Example

Expand Tex2Img_1402541222 up to powers of 2.

Using TI 84 Plus (OS 2.55)

maclaurin

From G.C,

f(0)= 3/2

f'(0) = -3/4

f”(0)= 5/4

Therefore using Maclaurin’s series expansion,

Tex2Img_1402541502

If powers higher than 2 such as 3 are required, then do differentiation to find the first derivative. Then enter into Y1. Y2 and Y3 will then give the second and third derivative.

Quick binomial expansion using GC

Binomial expansion can be done quickly using the GC.

Consider binomial expansion of Tex2Img_1396931745, where a is a real number, and q is a fraction or negative integer.

The recurrence formula for the coef works out to be

Tex2Img_1396931939

Example 1

Expand Tex2Img_1396932117  in ascending powers up to and including the term in Tex2Img_1396932205

Using TI 84 Plus (OS 2.55)

bin

Therefore, the expansion is

Tex2Img_1396933315

 

The recurrence formula can also be used to expand in descending powers of x.

Example 2

Expand Tex2Img_1397528779 in descending powers of x up to the 7th term.

Using TI 84 Plus (OS 2.55)

1

Therefore, the expansion is

Tex2Img_1397529466

 

Using GC to determine the nature of stationary points

Suppose we are required to determine the nature of stationary points for the following:

y

Using TI-84 Plus (OS 2.55) det

Observation of stationary points:

Left stationary point: First derivative changes from +ve to -ve. Therefore, it is a maximum point

Middle stationary point: No change in sign of deriative. Therefore, it is a point of inflexion.

Right stationary point. First derivative changes from -ve to +ve. Therefore, it is a minimum point

How to quickly find the intersection between planes

Finding the intersection between planes is typically 4 marks in A level exam, and can be solved using this method in 1 min 🙂

For example, find the line of intersection of r. ( 1 1 0 )=3 and r.(-1 -1 2 )= 7

Basically, we are finding the solution of these two equations:

x+y = 3

-x-y+2z = 7

Use TI 84 plus calculator.

sol

so we have

x= 3-y

y= y

z=5

So the line of intersection is r = (3 0 5) + a(- 1 1 0),  where a is a real number.