For the following data, use Gauss backward difference method to obtain the interpolating polynomial f(x):
| x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 |
| f(x) | 1.40 | 1.56 | 1.76 | 2.00 | 2.28 |
Hence, find the value of f(0.45).
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Let G be an infinite group such that for any non-trivial subgroup H of . Then prove that
i) or H is infinite;
ii) If , then o(g) is infinite.
Find the interpolating polynomial by Newton’s divided difference formula for the following data:
| x | 0 | 1 | 2 | 4 |
| y | 1 | 1 | 2 | 5 |
Divide the polynomial
x5 - 6x4 + 8x3 + 8x2 + 4x - 40
by (x - 3) by the synthetic division method and find the remainder.
Prove that every non-trivial subgroup of a cyclic group has finite index. Hence prove that is not cyclic.
गर्शगोरिन परिबंधों का प्रयोग करके आव्यूह$
के आइगेनमान आकलित कीजिए।
ऑयलर विधि से आदि मान समस्या को हल कीजिए$
लेते हुए y(3.1) ज्ञात कीजिए।
क) और
लेकर समलंबी नियम द्वारा
का मूल्यांकन कीजिए। रॉम्बर्ग विधि द्वारा
का सर्वोत्तम मान ज्ञात कीजिए।