I-Calculator ye-3D Graphing
I-plot i-z = f (x, y) e-3D exhunywe — ujikeleze futhi ukhulule, mahhala ku-inthanethi.
Dlulisa indawo yokudweba ukuze ujikeleze. eg. x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)
Malunga nale khadi
A 3D graphing calculator plots a surface defined by z = f(x, y) as a rotatable wireframe. Enter an expression in x and y, such as sin(x) * cos(y) or x^2 - y^2, and drag to orbit the surface in three dimensions. Useful for visualising multivariable functions, saddle points and peaks.
The calculator sweeps x and y across a grid, evaluates your expression at each grid point to get a height z, and connects those heights into a mesh that stands up off the flat xy-plane. Dragging orbits the camera around the surface so you can look at it from any angle, and the zoom control moves you nearer or further away. This turns an abstract two-variable formula into a shape you can actually see — hills, valleys, ridges and the pass-shaped saddle points where a surface rises in one direction while falling in another.
For a worked example, z = x^2 - y^2 draws the classic saddle (Pringle) surface: along the x-axis it curves upward like a valley, while along the y-axis it curves downward, meeting at a saddle point at the origin. By contrast z = sin(x) * cos(y) produces a regular egg-carton of alternating bumps and dips. It is used in multivariable calculus to picture partial behaviour, locate maxima, minima and saddle points, and understand the geometry of a function of two variables.
Imibuzo ebuzwa kaningi
Ngiza kanjani kumsebenzi we-3D?
Bhala uphawulo ku x kanye no y, isibonelo x^2 - y^2 noma sin(x) *cos(y). I-calculator ibhekana ne-grid futhi izoba nomphetho we-surface.
Ingabe ngizojikelezisa indawo?
Yebo. Dlulisa indawo ukuze uyijikeleze, bese usebenzisa ukulawula okuzobe kukhulisa ukudlulisa eduze noma eduze.
Yini okushoyo u-z = f(x, y)?
Kuthiwe ukuthi ubude z bendawo esitezi ngasinye busebenza kusuka ku x ne y ukuxhuma kweso sithembiso. Wonke (x, y) eplanethi ehlanzekile uthola ubude, futhi ama-heights ahlanganisana adala indawo.
Ngizodweba kanjani isikhala sesidlele?
Ngeza x^2 - y^2. Inyuka ngaphaya komgwaqo owodwa futhi iwela ngaphaya komgwaqo owodwa, ihlangana endaweni yesethi eqaleni — umdwebo ojwayelekile wendawo eyisizinda esingaba yi-peak noma i-valley khona.
Yini izinhlobo zesikhala esingabonakali?
Noma yini ongayibhala njengenhlamvu ye x ne y: iparaboloids (x^2 + y^2), izisekelo (x^2 - y^2), izimo ezibandayo (sin(x)*cos(y)) kanye nokuxhuma kwe-trigon, amandla, izimpande kanye ne-log.
Yini oyenzayo le divayisi ehlukile ku-2D graphing calculator?
Ithuluzi le-2D lizodweba i-y = f(x) njengegobolondo kwi-grid eqinile. Le thuluzi le-3D lizodweba i-z = f(x, y) njengendawo engaphakathi, ngakho libonisa ukuthi ixabiso lixhomekeke ku-inputs amabili ngasikhathi sinye ngaphezu kwesinye.
Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.