Cubic at 2
- f(x)
- x^3 - 3x
- x
- 2
- f(x)
- 2
Источник проверки: 8 − 6
Графический калькулятор
Стройте несколько функций, полярные и параметрические кривые; перемещайте и масштабируйте график; находите корни, пересечения, экстремумы и площади.
Обновлено Проверенные примеры: 3
Functions
y = x^2 plots a function; r = 1 + cos(θ) a polar curve; (cos(t), sin(2t)) a parametric curve. Trig uses radians here.
Points of interest in view
| Point | x ≈ | y ≈ |
|---|---|---|
| Root | −1.7320508 | 0 |
| Root | 0 | 0 |
| Root | 1.7320508 | 0 |
| Maximum | −1 | 2 |
| Minimum | 1 | −2 |
| Root | −6.2831853 | 0 |
| Root | −3.1415927 | 0 |
| Root | 3.1415927 | 0 |
| Root | 6.2831853 | 0 |
| Minimum | −7.8539816 | −2 |
| Maximum | −4.712389 | 2 |
| Minimum | −1.5707963 | −2 |
| Maximum | 1.5707963 | 2 |
| Minimum | 4.712389 | −2 |
| Maximum | 7.8539816 | 2 |
| Intersection | −1.981305 | −1.8338359 |
| Intersection | 0 | 0 |
| Intersection | 1.981305 | 1.8338359 |
Found by bisection on sign changes in double precision; shown to 8 significant figures.
О калькуляторе: Графический калькулятор
Plot up to six functions of x on one set of axes, alongside polar curves such as r = 1 + cos(θ) and parametric curves such as (cos(t), sin(2t)). Drag to pan, scroll or pinch to zoom, and hover to read each function's value, which is recomputed in 50-digit decimal at the pointer.
Below the plot, the calculator lists the roots, turning points and intersections visible in the current window, found by bisection on sign changes. It can also plot the derivative of the first function and shade the area under it between two limits, reporting the integral by Simpson's rule.
Trigonometric functions take radians here, as in most graphing software; type pi/2 rather than 90.
Примеры с решением
Sine at π/2
- f(x)
- sin(x)
- x
- pi/2
- f(x)
- 1
Источник проверки: sin(π/2) = 1; the plotter works in radians
Rational function
- f(x)
- 1/(x-1)
- x
- 3
- f(x)
- 0.5
Источник проверки: 1/2
Вопросы
How do I find where two graphs intersect?
Enter both functions and look at the 'Points of interest' table under the plot. It reports numerical candidates in the visible window, with coordinates rounded to 8 significant figures; this display precision does not guarantee that accuracy. Sampling can miss tangencies or closely spaced intersections. Zoom or pan to inspect the region, and check important solutions in the original equations.
Can it plot polar and parametric equations?
Yes. Start a line with r = to plot a polar curve in θ (for example r = 2 sin(3θ) draws a three-petal rose), or write a pair in brackets such as (cos(t), sin(t)) for a parametric curve, traced for t from −2π to 2π.
Why does tan(x) have gaps?
tan(x) has vertical asymptotes at x = π/2 + kπ, where it jumps from +∞ to −∞. The plotter breaks the line wherever consecutive samples jump by more than one and a half screen heights, so it doesn't draw false vertical lines across the asymptotes.
Насколько точен «Графический калькулятор»?
Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 3. Например, «Cubic at 2» проверяется по источнику 8 − 6.
Откуда взята методика?
OpenStax Precalculus 2e — Functions, function notation and graphs; Implementation: adaptive sampling with discontinuity breaks; values at a point recomputed in 50-digit Decimal.