# आलेख कॅल्क्युलेटर

> अनेक फलने, ध्रुवीय व प्राचलिक वक्र काढा; आलेख हलवा व झूम करा; मुळे, छेदनबिंदू, चरमबिंदू आणि क्षेत्रफळे शोधा.

परस्परसंवादी आवृत्ती: https://www.calcopenly.com/mr/math/graphing-calculator
विषय: गणिताचे कॅल्क्युलेटर

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.

## इनपुट

- **f(x)**
- **x**

## निकाल

- f(x) — मुख्य निकाल

## सोडवलेली उदाहरणे

### Cubic at 2

- f(x): x^3 - 3x
- x: 2
- **f(x): 2**
- पडताळणीचा स्रोत: 8 − 6

### Sine at π/2

- f(x): sin(x)
- x: pi/2
- **f(x): 1**
- पडताळणीचा स्रोत: sin(π/2) = 1; the plotter works in radians

### Rational function

- f(x): 1/(x-1)
- x: 3
- **f(x): 0.5**
- पडताळणीचा स्रोत: 1/2

## प्रश्न

### 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.

### “आलेख कॅल्क्युलेटर” किती अचूक आहे?

अचूकता तुमच्या इनपुटवर आणि पद्धतीच्या गृहीतकांवर अवलंबून असते. दशांश गणना 50 सार्थ अंक वापरते, पण अंदाज, संख्यात्मक पद्धती आणि मूळ डेटा कमी अचूक असू शकतात; दाखवलेल्या मूल्यांचे पूर्णांकन केल्याने या मर्यादा दूर होत नाहीत. स्वतंत्र स्रोतांतील सोडवलेल्या उदाहरणांशी पडताळणी: ३. उदाहरणार्थ, “Cubic at 2” ची पडताळणी 8 − 6 याच्याशी केली आहे.

### या पद्धतीचा स्रोत कोणता?

OpenStax Precalculus 2e — Functions, function notation and graphs; Implementation: adaptive sampling with discontinuity breaks; values at a point recomputed in 50-digit Decimal.

## स्रोत

- [OpenStax Precalculus 2e — Functions, function notation and graphs](https://openstax.org/books/precalculus-2e/pages/1-1-functions-and-function-notation)
- Implementation: adaptive sampling with discontinuity breaks; values at a point recomputed in 50-digit Decimal