3D Graphing Calculator
Plot z = f (x, y) m'njira yogwirizana 3D — kuzungulira ndi zoom, ufulu pa Intaneti.
Sungani nkhope kuti muzungulire. e.g. x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)
Zachidule
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.
Mafunso ofunsidwa nthawi zambiri
Kodi ndingapeze 3D ntchito?
Type an expression in both x and y, for example x^2 - y^2 or sin(x)*cos(y). The calculator evaluates it across a grid and draws the resulting surface.
Kodi ndingasinthire nkhope?
Ndikofunika. Tiyeni titenge nkhope kuti tipite m'mphepete mwake, ndipo tigwiritsa ntchito kuyang'anira kwa zoom kuti tipite pafupi kapena kumbuyo.
Kodi z = f (x, y) kumatanthauza chiyani?
Izi zikutanthauza kuti z pamwamba pa nthaka pa nthawi iliyonse ndi ntchito kuchokera x ndi y coordinates kuti nthawi. Zonse (x, y) pa ndege yosalala adzakhala pamwamba, ndipo iwo pamwamba limodzi kusunga nthaka.
Kodi ndingatani kuti ndipange saddle surface?
Idzafika m'malo mwa x^2 - y^2. Idzafika m'malo mwa axis imodzi ndipo idzagwa m'malo mwa zina, kukumana pa saddle point pa origin — standard example of a surface that is neither a peak nor a valley there.
Kodi ndi mitundu iti ya masamba amene ndingawone?
Chomwekocho mungalembe ngati mawu m'ma x ndi y: paraboloids (x^2 + y^2), saddles (x^2 - y^2), ripples (sin(x)*cos(y)) ndi kuphatikizika kwa trigonometri, mphamvu, ma roots ndi logs.
Kodi ndi chiyani chomwe chimasiyana ndi 2D graphing calculator?
Chida cha 2D chimapanga y = f(x) ngati mzere wozungulira pa gridi yopanda malire. Chida cha 3D chimapanga z = f(x, y) ngati mtunda m'malo, choncho chimasonyeza mmene mfundo ilili pazolemba ziwiri nthawi imodzi, osati imodzi.
Zimenezi ndi zowerengera zokhudzana ndi malangizo amtundu uliwonse, si zokhudzana ndi ndalama, zamoyo kapena zokhudzana ndi ndalama.