सांशलेषिक विभाजन विधि का प्रयोग करके यह दर्शाइए कि 2, समीकरण का एक सरल मूल है।
दिया गया बहुपद p(x) = x⁴ − 2x³ + x² − x − 2 सांश्लेषिक विभाजन द्वारा x = _________ _________ ________ ____ ________ ________ ___ _________ __________ _______ _______ ______.
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Which of the following statements are true, and which are false? Give reasons for your answers.
i) If k is a field, then so is .
ii) If R is an integral domain and I is an ideal of R, then .
iii) In a domain, every prime ideal is a maximal ideal.
iv) If R is a ring with zero divisors, and S is a subring of R, then S has zero divisors.
v) If R is a ring and is of degree
, then f(x) has exactly n roots in R.
विश्रामावस्था से आरंभ कर रही एक गाड़ी का वेग पहले घंटे के लिए निम्नलिखित तालिका में दिया गया है। सिम्पसन का नियम लागू करके, इस घंटे में गाड़ी द्वारा तय की गई दूरी ज्ञात कीजिए :
For an ideal I of a commutative ring R, define. Show that
i) is an ideal of R.
ii) .
iii) in some cases.
The method
where N is a positive constant, converges to N1/3. Find the rate of convergence of the method.
Solve the initial value problem using Euler method
Find y(3.1) taking .
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 |
यदि , तो C1 और C2।