#### **Calculus Operations**

#### Differentiate()

The formats:

- differentiate(expression)
- differentiate(expression, var)

but the variable arument may be ommitted if there is only
one variable in the expresstion or if variable x is intended.
For example:

differrentiate(sin(x)*exp(x))
partial differentials can also be performed by specifying the intended variable,in the form,
differentiaite(function, variable),
for example:

differentiate(2x*y^2 + 3y + z,y) will
yield a solution for when the fuction is differentiated with respect to y while other
variables (x and z) are constants.

#### Integrate()

MathSend can provide solution to both definite and indefinite integrals to
compute an integral. Formats:

- integrate(expression)
- integrate(expression, variable)
- integrate(expression, variable, lower_limit, upper_limit)

For example,

integrate(3*y*x^4+8y) will
integrate expression with respect to x, while for other variables
the form

integrate(3*y/x^4+8yxz, y) will integrate with
respect to y.
Multiple integrals can also be performed by specifying the order of the variable,
for example integrate

integrate(3*y/x^4+8yxz, y, x,x,z
integrates the expression four times: first with
respect to y, second with respect to x, third with respect to x again, and fourth with respect to z.
For definite integrals, the format is : integrate(expression, variable, lower_limit, upper_limit),
for example

integrate(3*y/x^4+8yxz, y, 0, inf) will
integrate the expression with respect to y from 0 to infinity

#### Limit()

Mathsend utilize the Sympy module to compute Limits to a supplied fuction using Gruntz
heuristics and algorithm. Formats:

- limit(expression)
- limit(expression, variable)
- limit(expression, variable, lower_limit, upper_limit)

The format is limit(expression, variable, lower_limit, upper_limit).
For example:

limit(x*sin(1/x), x, inf)
#### Series()

Asymptotic series expansions can be computed with the series keywords.
The formats:

- series(expression)
- series(expression, variable)
- series(expression, variable, x
_{0}, upper_limit)

if the x

_{0} ans order values are not specified (that is, any of the first two formats)
x0 will be taken as 0 while the order as 6. For example:
series(sin(x)) computes the Taylor series of sin(x) up to the order of series; and for a higher order of
the series, say 9, use series(sin(x),0,9).
For a different initial value, say 2, with the solution required up to the 9th order of x, we have

series(sin(x), x, 2, 9).