__Mathematical Experiment 1 __

Solve the equation .

Solve the system of equations

Solve the system of equations

Find the numerical approximation of
**tan(1.2)+tan(3.4)**

Find the numerical approximation of calculatiing with 17 digits.

Solve the equation numerically.

Compute .

Define the square function
**f:=y->y^2 **
and then simplify the expression
**f(sin(x))+f(cos(x)).**

Construct a function
**g:=(x,y)->x*y**
of two variables that defines the multiplication of two numbers.

Compute the derivative of
**sin(x)/(1+x).**

Compute the
**4th derivative**
of
**sin(x)/(1+x).**

Compute
**diff((x+1)/(x*y+1),x$2,y$3).**

Compute the indefinite integral
**int(cos(x),x).**

Compute the indefinite integral of
**cos(x)**
from 1 to 2 and then find its approximate value.

Find the limit of
as
**x**
approaches 0.

Solve the differential equation

Solve the linear recurrence

Draw the graph of sin(x) for x from -6 to 6.

`> `
**plot(sin(x),x=-6..6);**

Draw the graph of for x from -2 to 2, y from -2 to 2.

`> `
**plot3d(x^2-y^2,x=-2..2,y=-2..2);**

Draw the curve whose equation in polar coordinate is
**cos(t)+cos(2*t)**
for t ranging from 0 to
.

`> `
**plot(cos(t)+cos(2*t),t=0..2*Pi,coords=polar);**

Draw the graphs of
and
ranging from 0 to
**together**
.

`> `
**plot([3*cos(t),2*sin(t)],t=0..2*Pi);**

Draw the curve given by the
**parametric equations**
.

`> `
**plot([cos(10*t),sin(11*t),t=0..2*Pi]);**