Filter
Top Products
62 Activities
Solving a System of Nonlinear Equations
Problem
Using a graph, solve the equation x
3
N2x=2cos(x). Stated another way,
solve the system of two equations and two unknowns: y = x
3
N2x and y =
2cos(x). Use ZOOM factors to control the decimal places displayed on the
graph.
Procedure
1. Press z. Select the default mode settings. Press o. Turn off all
functions and stat plots. Enter the functions.
2. Press q
4 to select 4:ZDecimal. The display shows that two
solutions may exist (points where the two functions appear to
intersect).
3. Press q ~
4 to select 4:SetFactors from the ZOOM MEMORY
menu. Set XFact=10 and YFact=10.
4. Press q 2 to select 2:Zoom In. Use |, ~, }, and † to move the
free-moving cursor onto the apparent intersection of the functions
on the right side of the display. As you move the cursor, notice that
the
X and Y values have one decimal place.
5. Press Í to zoom in. Move the cursor over the intersection. As you
move the cursor, notice that now the X and Y values have two
decimal places.
6. Press Í to zoom in again. Move the free-moving cursor onto a
point exactly on the intersection. Notice the number of decimal
places.
7. Press y / 5 to select 5:intersect. Press Í to select the first
curve and Í to select the second curve. To guess, move the trace
cursor near the intersection. Press Í. What are the coordinates of
the intersection point?
8. Press q
4 to select 4:ZDecimal to redisplay the original graph.