I-Calculator ye-3D Graphing
Yenza i-plot yomhlaba z = f( x, y) kwi-3D esebenza ngokudibanisa — ujikeleze ujonge, simahla kwi-intanethi.
Rhuqa ubuso bokugquma. i-e.g. x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)
Malunga nale Calculator
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 ebuza rhoqo
Ndiza kungena njani kwimisebenzi ye-3D?
Uhlobo lwesivakalisi kwi x kunye ne y, umzekelo x^2 - y^2 okanye sin( x) * cos( y). I kalkuli ivavanya ngaphezulu kwe gridi kwaye izoba umgangatho ofunyenwe.
Ndingajikelezisa umgangatho?
Ewe. Rhuqa umphezulu wephepha ukuze ujikeleze, kwaye sebenzisa ulawulo lobungakanani bephepha ukujika ufike kufutshane okanye uhambe kude.
Yintoni i z = f (x, y) ithetha?
Oku kuthetha ukuba ubude z bomhlaba kwincopho nganye busebenza ngaphandle kox kunye no-y olungelelanisiweyo wendawo. Yonke (x, y) kwiplanethi ethe tyaba ifumana ubude, kwaye abo bude badibanisa bavelisa umgangatho.
Ndizoba njani umgangatho wesaddle?
Ngenisa i x^2 - y^2. Inyuka ngaphaya komgca omnye wesantya esiphezulu kwaye iwela ngaphaya komnye, idibana kwincopho yesaddle ekuqala - umzekelo oqhelekileyo womhlaba ongaphaya kwesantya esiphezulu okanye umlambo apho.
Yintoni iindidi zezinto eziphezulu endinokuzijonga?
Nantoni na ongayibhala njengentsingiselo kwi x ne y: iparaboloids (x^2 + y^2), i saddles (x^2 - y^2), i ripples (sin( x) * cos( y)) kunye nokudibanisa kwe trig, amandla, iziqhamo kunye ne logs.
Ihlukile njani le kwi-2D graphing calculator?
Isixhobo se-2D sizoba i-y = f(x) njengegophe kwi-grid ethe tyaba. Eli sixhobo se-3D sizoba i-z = f(x, y) njengendawo ejikelezayo kwisithuba, ngoko sibonisa ukuba ixabiso lixhomekeke kwizinto ezimbini ezingeniswayo ngexesha elinye kunokuba linye.
Results are estimates for general guidance only, not financial, medical or tax advice.