Calculus involves operations that are performed to study the various properties of any function, including rates of change, the limit behavior of a function, and calculation of the area under a function graph. In this section, you will learn the concepts of limits, derivatives, summation of series, and integrals. The following program uses limit functions to solve simple limit problems:

from sympy import limit, oo, symbols,exp, cos

oo+5
67000 < oo
10/oo

x , n = symbols ('x n')
limit( ((x**n - 1)/ (x - 1) ), x, 1)

limit( 1/x**2, x, 0)
limit( 1/x, x, 0, dir="-")

limit(cos(x)/x, x, 0)
limit(sin(x)**2/x, x, 0)
limit(exp(x)/x,x,oo)

Any SymPy expression can be differentiated using the diff function with the diff(func_to_be_differentiated, variable) prototype. The following program uses the diff function to compute the differentiation of various SymPy expressions:

from sympy import diff, symbols, Symbol, exp, dsolve, subs, Function

diff(x**4, x)
diff( x**3*cos(x), x )
diff( cos(x...