Kalkaaliyihii 3D Graphing
Qora dusha z = f (x, y) in 3D interaction — wareega iyo zoom, free online.
Jiidi daboolka si aad u wareegto. tusaale ahaan x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)
Ku saabsan Kalkaaliyahan
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.
Su'aalaha badanaa la isweydiiyo
Sideen u galaya shaqadii 3D?
Ku qor hadalka labada x iyo y, tusaale ahaan x^2 - y^2 ama sin (x) * cos (y). Kalkulatorku wuxuu qiimeeyaa iyada oo ku wareegsan grid iyo u saaran yahay dhumucda ka soo baxda.
Ma ku wareegi karaa dhulka?
Haa. Ku riix daboolka si aad u wareegto, oo isticmaal xakamaynta zoom si aad u dhaqaaqdo si dhow ama ka fog.
Maxaa z = f (x, y) ka dhigan tahay?
Waxay ka dhigan tahay in dhererka z ee dhulka oo ah dhibcood kasta oo ka shaqeeyaan x iyo y coordinates. kasta (x, y) on diyaaradda flat hesho dhererka, iyo dhererka kuwaas oo wada abuuraan dhulka.
Sideen u abuuraa muuqaalka saddle?
X^2 - y^2. Waxay kor u kacdaa xagal mid ah, waxayna hoos u dhacdaa xagal kale, waxayna ku kulmaan meel saddle ah oo asalka ah — tusaale caadi ah oo ah dhul aan aheyn xagal ama dooxada halkaas.
Maxaa noocyada daaqadaha aan ka arki karaa?
Wax kasta oo aad ku qorto sida eray x iyo y: paraboloids (x ^ 2 + y ^ 2), saddles (x ^ 2 - y ^ 2), ripples (sin (x) * cos (y)) iyo isku dhafka trig, awoodaha, root iyo logs.
Sidee ayaa tan ka duwan tahay 2D graphing xisaabinta?
2D qalabku wuxuu ku tuuraa y = f (x) sida xagal ku yaal xargaha siman. 3D qalabku wuxuu ku tuuraa z = f (x, y) sida dhul meel, sidaas darteed wuxuu muujinayaa sida qiimaha ku xiran yahay laba soo gelitaanka isla markiiba ka badan mid.
Natiijooyinka waa tirakoobka loogu talagalay tilmaamaha guud oo keliya, maaha dhaqaale, caafimaad ama talo bixin canshuur.