3D graphing calculator
Pọtụ̀ elu z = f(x, y) n'ime 3D n'ime - tụgharịa na zuum, n'efu n'ịntanetị.
Kpụga n'elu ahụ ka ịtụgharị. eg x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)
N'ihe banyere calculator a
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.
Ajụjụ ndị a na-ajụkarị
Olee otú m ga-esi tinye 3D ọrụ?
Tinye nkọwa n'ime x na y, dịka ọmụmaatụ x^2 - y^2 mọọbụ sin(x)*cos(y). Kalọnaịlụ ahụ na-enyocha ya n'ime grìíị̀ nakwa na-edepụta n'ime n'ime.
Enwere m ike ịtụgharị n'elu?
Ee. Dọọ n'eluigwe ka ọ kpụga n'okporo ụzọ ya, na jiri nlezianya zuum ka ịkpụga n'ebe dị nso mọọbụ n'ebe dị anya.
Gịnị bụ z = f(x, y)?
Ọ pụtara na elu z nke eluigwe na mpaghara ebe ọbụla ejirila ya n'ime site na x na y coordinates nke mpaghara ebe ahụ. Ha niile (x, y) na flaịd plane na-enweta eluigwe, na eluigwe ndị ahụ na-ejikọta ya na eluigwe.
Olee otú m ga-esi kpụga saịlị n'elu?
Tinye x^2 - y^2. O na-awụsa n'akụkụ otu axis ma pụta n'akụkụ nke ọzọ, na-emekọrịta na saịdị bọtịn na origen - ihe atụ nke eluigwe nke abụghị peekà ma ọ bụ váìlì ebe ahụ.
Kedu ụdị n'ime eluigwe m ga-ahụ?
Ihe ọbụla ị ga-edebe dịka nkọwa na x na y: paraboloids (x^2 + y^2), saddles (x^2 - y^2), ripples (sin(x)*cos(y)) na n'omume nke trigs, powers, roots na logs.
Olee otú ọ dị iche na 2D graphing calculator?
2D tulee na-egosipụta y = f(x) dịka kurva na flaịt grììtì. 3D tulee a na-egosipụta z = f(x, y) dịka n'eluigwe na ebe, ya mere ọ na-egosi otú váìlì ahụ si dabere na inyogo abụọ n'otu oge kama otu.
Ihe a na-ahụta bụ n'ihi nlekọta n'ozuzu ya, ọ bụghị nlekọta ego, ọgwụ ma ọ bụ nlekọta ego.