1 Plotting Functions

1.1 Ordinary Functions

To plot a function, for example f(x) = sinx, in theinput box type f(x)=sin(x) or y=sin(x) or simplysin(x)

To Do

• plot the functions xn

Hint: Create a slider for n

• Plot the functions ex, sin( 1x ), |x|, sin tanx

• Plot x sin( 1x ) and y = x y = −x on the same

window and watch the function at (0,0)

1.2 Implicit Functions

Only implicit polynomial functions can be draw usinggeogebra

To Do

• plot x2 + y2 + xy − 3 = 0

• plot x99y − y99x = 1

• Try to plot x23 + y

23 = 1

Hint: Not Possible using implicit plot

1.3 Parametric Plot

The syntax iscurve[xfunction, yfunction, parameter,

startvalue, endvalue]

For example to plot x = cos t, y = sin t, in the inputbox, type curve[sin(t),cos(t),0,2pi]

To Do In the Calculus(Anton) book do some exer-cise problems–page 701 Qn.23

1.4 Polar Plot

There is no direct option for polar plot, parametricplot can be used to plot polar relations like r = f(θ).For, first define the function f(x) and then typecurve[f(t)cos(t),f(t)sin(t),t,0,10]

To Do

• Plot r = cos(θ) and r = 1 + cosθHint: Type f(x)=cos(x) hit enterthen curve[f(t)cos(t),f(t)sin(t),t,0,2pi]

then change f(x)=1+cos(x)

• Plot r = cos(2θ)Hint: Create a slider s from 0 to 2π,for the end value of t, Then type curve

[f(t)cos(t), f(t)sin(t),t, 0,s]

Then change the slider and verify the path

2 Taylor’s series of sinx

To get the Taylor’s series of a functionTaylorPolynomial[ <Function>, <x-Value>,

<Order Number> ] if x-value is 0 we get the seriesabout x = 0 and the order number is the highestpower of x term

To Do Draw the Taylor’s series of sinx and Createa slider for the order number and change the slider

3 Piece-wise Functions

Use If[ <Condition>, <Then>, <Else> ]

For example if[x<pi, cos(t), sin(t)] for

f(x) =

{cosx if x < pi

sinx if x > pi

To Do

• Plot the function sinx for −π < x < π

• Reflect the function about y = x using reflecttool to get the graph of sin−1 x

• Plot the graph of cos−1 x

• Plot the graphs of ex and log x on the same win-dow

4 Derivative

The derivative syntax is Derivative[ <Function>,

<Number> ]. If the number is 2 we get the secondderivative.

To Do

• Draw the graph of x2 sin( 1x )

• Draw the derivative of the above function

5 Upper Sum and Lower Sum

ExerciseThank You