Àwọn Ìṣàmúlò-ètò 3D

Fi ojú-ìwé z = f(x, y) pamọ́ sínú àwọn àgbékalẹ̀ 3D - ìṣàfarawé àti ìṣàmúlò-ètò, àìfihàn lórí intanẹ́ẹ̀tì.

z = f(x, y)

Àwọn Ìjánu-ìsún ±

Gbé àwọn ààyè-iṣẹ́ lọ́wọ́lọ́wọ́ láti yipada. gẹgẹ bi x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)

Àkóónú ìṣàmúlò-ètò yìí

the 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 visualizing multivariable functions, saddle points and peaks. Dragging orbits the camera around the surface so you can look at it from any angle, and the zoom control moves you closer 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. This turns an abstract two-variable formula into a shape you can actually see.For example, z = x^2 - y^2 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.The 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 visualizing multivariable functions, saddle points and peaks.

Àwọn Àtòjọ-ẹ̀yàn

Bawo ni mo ṣe lè fi àwọn ìṣàmúlò-ètò 3D pamọ́?

Ṣàfihàn àwọn àkóónú nínú x náà àti y, àwọn àkóónú bíi x^2 - y^2 tàbí sin(x)*cos(y). Àwọn àkóónú náà ń fi àwọn ààyè ààyè pamọ́ sí àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè àwọn ààyè

Ń lè fi ààyè ààyè náà pamọ́?

Ya. Tọ́ ààyè láti fi pamọ́, àti ló àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò láti mú ìsàlẹ̀-ètò náà láti sàlú àwọn ààyè náà.

Kini z = f(x, y) tumọ si?

O tumọ̀ si pé ìsàlẹ̀ z tí awájú nínú àwọn ààyè-iṣẹ́ nínú àwọn ààyè-iṣẹ́ nínú àwọn ààyè-iṣẹ́ nínú gbogbo wọn ní a tí ṣe àwọn àwọn ààyè-iṣẹ́ x atí y tí a tí n ṣiṣẹ́ nínú àwọn ààyè-iṣẹ́ náà. Gbogbo (x, y) nínú àwọn ààyè-iṣẹ́ tí a tí n gbọ́dọ̀ nínú àwọn ààyè-iṣẹ́ náà gbá ìsàlẹ̀, àtí àwọn ìsàlẹ̀ náà ní pàtó nínú àwọn ààyè-iṣẹ́.

Bawo ni mo ṣe lè fi ààyè ààyè sáà hàn?

Fi x^2 - y^2 pamọ́. Ó kù ní pàtó ásìsì kan àti àwọn ìsàlẹ̀ ní pàtó ní pàtó àwọn mìíràn, tí a bá gbọ́ nínú àwọn ààyè sáà nínú ìṣàmúlò-ètò - àwọn ààyè ìṣàmúlò-ètò tí a lò nínú ojú-ìwé tí kò jẹ́ ààyè àti àgbègbè nínú.

Àwọn irúfẹ̀nù àwọn ojú-ìwé wò ní mò lè wò?

Àkóónú kan tí o lè kọ́ bí àwọn ìṣàfilọ́lẹ̀ nínú x atí y: paraboloids (x^2 + y^2), saddles (x^2 - y^2), ripples (sin(x)*cos(y)) àtí àwọn ìṣàmúlò-ètò tí a lò nínú trige, powers, roots àtí logs.

Bawo ní yìí ṣe yatọ si àwọn ìṣàmúlò-ètò àwọn ààtò àtòjọ-ẹ̀yàn 2D?

Àtòjọ-ẹ̀yàn 2D náà ń fi y = f(x) pamọ́ láti inú àwọn ìṣàmúlò-ètò àwọn ààyè-iṣẹ́. Àtòjọ-ẹ̀yàn 3D yìí ń fi z = f(x, y) pamọ́ láti inú àwọn ààyè-iṣẹ́ àwọn ààyè-iṣẹ́, láti fi fihan bí àwọn fálù ṣe ń dáju àwọn ìṣàmúlò-ètò mejì nígbà kan jú ọkan lọ.

Àwọn àwọn

Àkóónú ìṣàmúlò-ètò yìí

Àwọn Àtòjọ-ẹ̀yàn

Àwọn Ìṣàmúlò-ètò Ìṣàmúlò-ètò