Cubic at 2
- f(x)
- x^3 - 3x
- x
- 2
- f(x)
- 2
جانچ کا ماخذ: 8 − 6
گراف بنانے کا کیلکولیٹر
کئی تفاعل، قطبی منحنیات اور پیرامیٹری منحنیات بنائیں؛ گراف کو حرکت دیں اور زوم کریں؛ جذر، نقاطِ تقاطع، مقامی زیادہ سے زیادہ اور کم سے کم نقاط اور رقبے معلوم کریں۔
تازہ کاری جانچی گئی مثالیں: 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.
گراف بنانے کا کیلکولیٹر کے بارے میں
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.
حل شدہ مثالیں
Sine at π/2
- f(x)
- sin(x)
- x
- pi/2
- f(x)
- 1
جانچ کا ماخذ: sin(π/2) = 1; the plotter works in radians
Rational function
- f(x)
- 1/(x-1)
- x
- 3
- f(x)
- 0.5
جانچ کا ماخذ: 1/2
سوالات
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.
“گراف بنانے کا کیلکولیٹر” کتنا درست ہے؟
درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 3۔ مثلاً، “Cubic at 2” کو 8 − 6 سے جانچا جاتا ہے۔
اس طریقے کا ماخذ کیا ہے؟
OpenStax Precalculus 2e — Functions, function notation and graphs; Implementation: adaptive sampling with discontinuity breaks; values at a point recomputed in 50-digit Decimal.