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Analysis |
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Analysis is the area of mathematics devoted to the study of functions.
To differentiate use the Clicking on the The differentiate command takes 2 arguments; the first corresponds to the expression to be differentiated and the second to the variable with respect to which we wish to differentiate. In the case of a function of a single variable, the second argument may be omitted.
The ' sign can be used after the expression to be derived, in accordance with normal mathematical notation. Note that here there is no need to state the variable with respect to which we are differentiating, because wiris will identify it automatically. If this operator is applied to an expression with more than one variable, an error is returned.
The ' sign can also be used to differentiate functions. In fact, if f=f(t) is a function of a single variable f' is the derivative of f with respect to t). Therefore, the derivative of f at point a is f'(a) in accordance with normal analysis notation. Let's look at some examples.
Integral calculus To obtain the antiderivative or indefinite integral of a given function, we use the Icon Clicking on the Alternatively the integrate command can be used with two arguments, the first corresponding to the expression and the second to the variable.
If there is no doubt about the variable of integration, the indefinite integral of the function can also be obtained using the icon, If the expression to be integrated has no variables, wiris will integrate it with respect to a made up variable. If there is only one variable, it will be integrated with respect to it, and if there is more than one, an error will be returned. In all cases, the result is a primitive function of the argument. Alternatively, the integrate command can be used, with a single argument, instead of the
Definite integral To calculate the definite integral between two limits, use the Upon clicking the Alternatively the integrate command can be used with four arguments. The first corresponds to the expression, the second to the variable and the third and fourth correspond to the lower and upper limits of integration, respectively.
Where there is no doubt about the variable of integration, the definite integrals of functions can be obtained using the icon Alternatively the integrate command can be used with three arguments. The first corresponds to the function or expression to be integrated and the second and third correspond to the upper and lower limits of integration, respectively.
To calculate function limits, use the Limit Upon clicking the limit(f,x,a) ![]() The value for a can be a real number, positive infinity (the
Horizontal limit The To calculate right and left limits, use the command limit. To calculate the limit of function f when x approaches a from the right (or from the left), either of the two following expressions can be used: limit(f,x,a,1) (from the left, limit(f,x,a,-1) )
wiris supports calculation of the Taylor Series of a real function at a given point. To calculate the Taylor Series of a function at a given point, use the taylor_series command with three arguments. The first argument corresponds to the function, the second to the variable and the third corresponds to the value for which the Taylor Series should be calculated (remember that the Taylor Series permits us to approximate the value of any function at a given point). If you would like to view a specific number of terms of the series, which is infinite, specify this number in the fourth argument.
In order to obtain the Taylor polynomial of a given order for a particular function, use the taylor command, followed by the four arguments just described. Note, the fourth argument is necessary for this purpose.
wiris allows us to determine whether a series is convergent, as well as calculating the sum of a convergent series. Use standard mathematical notation to express the series, as shown in the following examples. The response will give the value for the sum of the series if it is convergent (or if it is divergent, but wiris knows how to calculate the relevant infinite value), and the series itself in other cases. To ask wiris about whether a series is convergent or divergent, use the convergent? command, and enter the series as the only argument.
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