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Maths Helper Plus is a very powerful function plotter. See the 'Example Graphs' page to see for yourself. Also see 'Animations' for examples of using parameters in function plots.

Options for function graphs are listed below:Â

 Plot settings

Select plot colour, resolution, plot domain or 'plot as dots' option.
Choose to display any of: the function, its first derivative, and its second derivative.
Inequality shading uses an overlay technique so that a third colour occurs when two different regions overlap.

 Data table

Instead of a boring list of function values, this feature allows you to enter a list of expressions that will be evaluated to create the table. Enter a list of 'x' values at which to evaluate the table expressions. You can even use a special 'series operator' to simplify this task. Enter a list of expressions to use as table headings, and choose to display first and second derivatives in the table if required. Here is a table of values plotted on the text view for the function: y = 3x² - 2x + 4. The function header expressions were: 3x²,Â  2x,Â  4, and y:

xÂ Â  3x²Â  2xÂ Â  4Â Â  y
-5Â  75Â Â  -10Â  4Â Â  89
-4Â  48Â Â  -8Â Â  4Â Â  60
-3Â  27Â Â  -6Â Â  4Â Â  37
-2Â  12Â Â  -4Â Â  4Â Â  20
-1Â  3Â Â Â  -2Â Â  4Â Â  9
0Â Â  0Â Â Â  0Â Â Â  4Â Â  4
1Â Â  3Â Â Â  2Â Â Â  4Â Â  5
2Â Â  12Â Â  4Â Â Â  4Â Â  12
3Â Â  27Â Â  6Â Â Â  4Â Â  25
4Â Â  48Â Â  8Â Â Â  4Â Â  44
5Â Â  75Â Â  10Â Â  4Â Â  69

 Tangents & Normals

Type a list of 'x' values at which to calculate tangent lines for the function, or normal lines for the function. The 'expanded working' option displays the calculation steps on the text view. Buttons provided to plot the tangent and normal lines. Here are some calculations displayed on the text view by this option:

TANGENT line at x = 2
At x1 = 2, y1 = 0.8
and the gradient, m = dy/dx = 0.8
The equation of the tangent at (x1,y1) is given by:

Â y - y1 = m(x - x1)
Â Â  so y = m(x - x1) + y1
Â Â Â Â Â Â Â  = mx - mx1 + y1
Â Â Â Â Â Â Â  = mx + (y1 - mx1)
Â Â Â Â Â Â Â  = 0.8x + (0.8 - 0.8 × 2)

Â so y = 0.8x - 0.8

NORMAL line at x = 1
At x1 = 1, y1 = 0.2
The gradient of the normal line is:
'M' = -(1/m) = -(1/0.4) = -2.5
The equation of the normal at (x1,y1) is given by:

y - y1 = M(x - x1)
Â  so y = M(x - x1) + y1
Â Â Â Â Â Â  = Mx - Mx1 + y1
Â Â Â Â Â Â  = Mx + (y1 - Mx1)
Â Â Â Â Â Â  = -2.5x + (0.2 - -2.5 × 1)

Â so y = -2.5x + 2.7

 Integrals

Type a set of limits of integration for the function, like this: [1,pi] [4,2pi], then type a list of numbers of intervals for the numerical techniques.Â

Choose as many of these integration techniques as you like: Simpson's rule, Trapezoidal rule, Left, Mid-point, or Right rectangles. If required, calculate true area instead of the definate integral.Â

Also choose to shade the areas and set the shading colour. (See picture below:)Â

The results are tabulated on the text view like this:

 Definite integral from x = 1 to x = pi nÂ  SimpsonÂ Â  TrapezoidalÂ Â  Left RectanglesÂ Â  MidpointÂ Â  Right Rectangles 2Â  2.00042Â Â  2.08227Â Â Â Â Â Â  1.13252Â Â Â Â Â Â Â Â Â Â  1.95949Â Â Â  3.03202 4Â  2.00042Â Â  2.02088Â Â Â Â Â Â  1.546Â Â Â Â Â Â Â Â Â Â Â Â  1.99019Â Â Â  2.49576 8Â  2.00042Â Â  2.00553Â Â Â Â Â Â  1.7681Â Â Â Â Â Â Â Â Â Â Â  1.99786Â Â Â  2.24297 50 2.00042Â Â  2.00055Â Â Â Â Â Â  1.96256Â Â Â Â Â Â Â Â Â Â  2.00035Â Â Â  2.03854 Definite integral from x = 4 to x = 2pi nÂ  SimpsonÂ Â  TrapezoidalÂ Â  Left RectanglesÂ Â  MidpointÂ Â  Right Rectangles 2Â  12.27Â Â Â Â  12.3692Â Â Â Â Â Â  9.68892Â Â Â Â Â Â Â Â Â Â  12.2204Â Â Â  15.0495 4Â  12.27Â Â Â Â  12.2948Â Â Â Â Â Â  10.9547Â Â Â Â Â Â Â Â Â Â  12.2576Â Â Â  13.6349 8Â  12.27Â Â Â Â  12.2762Â Â Â Â Â Â  11.6061Â Â Â Â Â Â Â Â Â Â  12.2669Â Â Â  12.9463 50 12.27Â Â Â Â  12.2702Â Â Â Â Â Â  12.163Â Â Â Â Â Â Â Â Â Â Â  12.2699Â Â Â  12.3774