efm algebra
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Algebra
Ahmad Syaiful Rizal 110210151001
Amalia Martha Santosa 110210151004
Brigita Febrianti 110210151019
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GEO GEBRA
GeoGebra is dynamic mathematics software that
combines geometry, algebra, and calculus.
This software is developed for teaching and
learning mathematics in schools by Markus
Hohenwarter at Florida Atlantic University.On the one hand, GeoGebra is a dynamic geometry
system.
You can do constructions with points, vectors,
segments, lines, conic sections, as well as
functions and change the outcome of the next
construction. On the other hand, equations andcoordinates can be entered directly. .
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APPLICATION OF GEOGEBRA
LINES
DERIVATIVES AND TANGENTLINE
RIEMANN SUM AND INTEGRAL
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LINES
There are two types of equation commonly used todescribe a line:
- Slope-intercept-Point-slope.
Both forms are really both variations on the same idea. Inboth cases is needed to know the coordinates of one
point, and the slope of the line. :
-In the slope-intercept form, the given point is always onthe y-axis and you supply the y-coordinate of that point(Its x-coordinate is always zero).
- In the point-slope form, you can use any point.
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INTERSECTION OF TWO LINE
The intersection of a line and aline can be the empty set, a point, or a
line. Distinguishing these cases andfinding the intersection point have use,for example, in computer graphics,motion planning, and collision
detection.
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y = 2x+3 and y=6x+7
FIND THE SLOPE ANDINTERSECTION OF TWO LINES ?
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FOR FINDING A SLOPE :
Slope[line]
FOR FINDING AN INTERSECTION OF TWO
LINES :
Intersect[object,obejct]
THE COMMAND
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DERIVATIVE
The definition of derivative of a function can be expressed by
I think all of you have already known about this
lim0
+ ()
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DERIVATIVE
Find the derivative of f(x) = 3x3 + 2x2 6x+ 5
1) type the equation in Input Barand press Enter
2) type this command (or choose from drop down list) in Input Barand press Enter
Or,
GeoGebra will determine the derivation in Algebra View and construct the curve f(x)
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DERIVATIVE
Find the derivative of f(x) = (3x2 5)4
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TANGENT LINE
A line that touches a curve at a point without crossing
over. Formally, it is a line which intersects a differentiable
curve at a point where the slope of the curve equals theslope of the line.
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Construct a tangent line at the graph off(x) = 2x3 + 3x 2
1) type the equation in Input Barand press Enter
2) choose New Point from Construction Tools and click at the graph
3) choose Tangents from toolbox and click at point and graph
4) Drag the point at the graph
TANGENT LINE
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TANGENT LINE
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RIEMANN SUM
Let a closed interval be partitioned by points < 1 < 2 < < 1 < , where the lengths of the resulting intervals between thepoints are denoted x1, x2, ..., xn. Let be an arbitrary point in
the th subinterval. Then the quantity (k)=
is called a Riemann sum for a given function () and partition, andthe value max xis called the mesh size of the partition.
. The shaded areas in the above plots show the lower and uppersums for a constant mesh size.
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RIEMANN SUM
What is it?
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RIEMANN SUM
Using geogebra
Approxiate and demonstrate the riemann sum for f(x) = 2x3
+8x2 + 4x 2 by taking the sampel point a = -3 and b = -1, and
n = 8. sketch the graph of function and use the geogebra to
determine the
1) type the equation in Input Barand press Enter
2) type this command (or choose from drop down list) in Input Barand press Enter
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RIEMANN SUM
Using geogebra
Command script in geogebra
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DEFINITE INTEGRAL
Definite integral is the number that magnitude is determined bytaking the limit of riemann sum, which is associated with a normclosedinterval partition approach
Determine the area under the graph of function
f(x) = 2x3 + 3x 2 with the boundary x = -3 dan x = -2
1) type the equation in Input Barand press Enter
2) type this command (or choose from drop down list) in Input Barand press Enter
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DEFINITE INTEGRAL
Determine the area under the graph offunction
4 3 + 1
with the boundary x = -1 dan x = 1.9
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THANKS FOR YOUR ATTENTION