इन सवालों के जवाब देकर एनर्जी कमाएं, फिर मछली पकड़ें और घूमें। कोई अकाउंट नहीं चाहिए।
शिक्षकों के लिए: Iteration and numerical solutions (Mathematics, Algebra) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके शिक्षार्थी लाइव गेम की तरह खेलें।
Iteration repeatedly applies a formula. A suitable formula and starting value may converge to a root; convergence is not guaranteed.
The notation is xn+1 = f(xn), starting from x0 or x1.
Using iteration
Rearrange an equation into the form x = f(x). For x3 - 3x - 1 = 0: x = \frac{x3 - 1}{3} or x = \√[3]{3x + 1}.
For xₙ₊₁ = ∛(3xₙ + 1), starting x₁ = 2 gives x₂ ≈ 1.912931 and x₃ ≈ 1.888835. Continuing converges to about 1.879385; retain calculator precision between steps.
Use the calculator's ANS key to repeat quickly, and keep full calculator accuracy until you round at the end.
Decimal search and change of sign
If f(a) and f(b) have opposite signs, a root of f(x) = 0 lies between a and b (for a continuous function).
Narrow down by testing the midpoint (the decimal search or interval bisection).
To show a root is 1.88 to 2 d.p., show f(1.875) and f(1.885) have opposite signs.
Stating the answer
Give the number of decimal places asked, but check the rounding by looking at when successive iterations agree.
Agreement between a few rounded iterates supports an estimate but is not a proof of accuracy. For a continuous function, a sign-changing interval within the required rounding limits brackets a root.
स्लाइड्स
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