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# MathHandbook Calculator

## int_0^oo MathHandbook dx = sum_(k=0)^oo MathHandbook.com

(zoom graph by mouse wheel)

How to use? There are many ways:

1. Input or click sin(x) , click for integration, click button for derivative to check its result, click again for second derivative, click to inverse a function, click for definition, click to simplify, click ......
2. Input the unkown y as seond argument,
o sin(x)=cos(y), y
then click the button to solve for unknown y.
3. Input command by use of the first function as command, e.g.
then hit the button or the ENTER key in your keybord.
4. Input function, e.g.
5. Input function by use of "," or ";" as separator for multistatements, e.g.
6. Input question mark ? to show a list of function, i.e.
7. Input function and question mark ? to show its function source. e.g.
 To do Button algebra 1st row simplify sin^((0.5))(x) expand (x-1)^2 factor (x^2-1) convert sin(x) to exp(x) convert exp(x) to sin(x) convert sin(x) to sinh(x) solve equation for x, solve( exp(x)+exp(-x)=1 ) calculus: default variable is x 2nd row convert sin(x) to integral limit lim( log(x)/x as x->oo ) differentiate d/dx sin(x) integrate ∫ sin(x) dx infinite integration integrate( exp(-x) as x->oo ) nth derivative formula d^n/dx^n sin(x) semiderivative d^(0.5)/dx^(0.5) sin(x) semiintegrate d^(-0.5)/dx^(-0.5) sin(x) dsolve solve (fractional) differential equation for y, dsolve( y'=(x-y)! ), dsolve d^0.5/dx^0.5 y=sin^((-0.5))(x) discrete math: default index variable is k 3th row convert sin(x) to sum Taylor series expansion taylor(sin(x)) series( sin(x) ) difference Δk^2 Indefinite sum ∑ 1/k^6 partial sum sum_(k=0)^n k partial sum sum_(k=1)^n k infinite sum sum( x^k/k! as k->oo ) infinite sum sum_(k=1)^oo x^k/k rsolve solve recurrence equation y(x+1)-y(x)=x Numeric math 4th row numeric solve equation nsolve( x^2-1=0 ) numeric limit lim _(x->0) sin(x)/x numeric integrate int _1^2 sin(x) dx numeric sum sum _(x=1)^8 x inverse( sin(x) ) definition( sin(x) ) Show function source. sin(x)? numeric answer Interactive Plot: zoom by mouse wheel 5th row Clear input polar plot polarplot(sin(4*x)) parametric plot parametricplot( x=sin(t) and y=cos(2*t) ) implicit plot x^2-y^2=2 and x-y=1 tangent plot tangentplot(sin(x)) secant plot secantplot(sin(x)) plot sin(x) and x^2 symbolic answer

The same color buttons are a pair of inverse operators, its result can be checked each other if it returns origial function or not. Usual keywords are lowercase, which are different from uppercase, e.g. sin is different from Sin. Its default variable is small letter x, but its default index variable in discrete math is k.

### Example:

• Add new function f(x) = x^2
f(x) = x^2

• Add new rule of derivative d/dx f(x_) := 2*x
d(f(x_), x_) := 2*x

• Add new rule of integral int f(x) dx := F(x)
integrate(f(x_), x_) := F(x)

• algebra: convert.
• calculus: limit, nth derivative, differentiation, integral, fractional calculus, convert to integral.
• equation: Inequalities, congruence equation, Dorphine equation, modulus equation, recurrence equation, (fractional) differential equation, (fractional) integral equation.
• discrete math: sum, partial sum, indefinite sum, infinite sum, convert to sum.
• numeric math:
• interactive plot: polar plot, parametric plot, implicit plot, tangent plot, secant plot, zoom by mouse wheel.

Please read its example and manual of symbolic computation Computer Algebra System.

## MathHandbook

What is mathHandbook?

It is an online graphic calculator and computer algebra system with learning. It can perform exact, numeric, symbolic and graphic computation, e.g. any order of derivative, fractional calculus, fractional differential equation, symbolic differentation and integration, indefinite sum, interactive plot. It is a programming language, e.g. add new fractional derivatives and integrals, conditional or recursive functions, procedures, and rules.
It can run on any mobile with Internet, and any computer with Java.
It is Computer Algebra System for symbolic computation of any order of fractional derivative. It has three versions:

1. Phone version: run on any phone online. It does not requires to download anything.