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- We will start with an intuitive solution, and then a rule can be built for solving general fractional inequalities. To make things e * [[Power mean inequality]]12 KB (1,806 words) - 05:07, 19 June 2024
- ...mation that one can have about a polynomial of one variable is the highest power of the variable which appears in the polynomial. This number is known as t ...ing about whether or not these roots are positive or negative. Descarte's Rule of Signs says that for a polynomial <math>P(x)</math>, the number of positi6 KB (1,100 words) - 14:57, 30 August 2024
- ...{p}</math>. Since <math>\text{gcd}\, (a,p) = 1</math>, by the cancellation rule, that reduces to <math>i \equiv j \pmod{p},</math> which means <math>i = j< .../math> as a product of cyclic groups of prime order where the set of prime power orders is unique. We can do this because if any two prime powers are not c15 KB (2,618 words) - 11:03, 19 February 2025
- === Divisibility Rule for 2 and Powers of 2 === [[Divisibility rules/Rule for 2 and powers of 2 proof | Proof]]10 KB (1,572 words) - 21:11, 22 September 2024
- ...> or to <math>n+2^{m_n+1}</math> where <math>2^{m_n}</math> is the largest power of 2 that is a factor of <math>n</math>. Show that if <math>k\ge2</math> is3 KB (520 words) - 08:24, 14 May 2021
- The derivative of <math>f(y)</math>, using the Power Rule, is ...[derivative]] of <math>f(x)</math> using the [[Chain Rule]] and [[Quotient Rule]], we have <math>\frac{\text{d}f(x)}{\text{d}x} = \frac{6y(3y+2)-(3y+2)^2}{5 KB (824 words) - 18:34, 20 July 2024
- We want the coefficient of the <math>y^2</math> term of each power of each binomial, which by the binomial theorem is <math>{2\choose 2} + {3\ ...}{dx^2} = 2\cdot 1 - 3\cdot 2x+\cdots-17\cdot 16x^{15}</math> by the power rule.6 KB (872 words) - 15:51, 9 June 2023
- ...question asks for proper divisors, we exclude <math>2^65^6</math>, so each power is actually <math>141</math> times. The answer is thus <math>S = \log 2^{14 .....</math> and so on equals <math>\log_{10} (abcd...)</math> by sum-product rule of logs, so the problem is reduced to finding the logarithm base 10 of the3 KB (487 words) - 19:52, 16 September 2020
- ...> or to <math>n+2^{m_n+1}</math> where <math>2^{m_n}</math> is the largest power of 2 that is a factor of <math>n</math>. Show that if <math>k\ge 2</math> i ...made from a number that is divisible by <math>2^M</math> (and by no higher power of 2). Thus we must have <math>M < i_0</math>, since otherwise a number div7 KB (1,280 words) - 16:23, 26 March 2016
- We can write a power series: <cmath>f(x)=\sum_{n=0}^{\infty} F_n x^n</cmath> Hint: let u=x-s and use the chain rule.6 KB (955 words) - 01:11, 5 February 2025
- ...le-lane highway, cars all travel at the same speed and all obey the safety rule: the distance from the back of the car ahead to the front of the car behind ...< 1000</math>, and <math>m</math> is not divisible by the <math>n</math>th power of any prime. Find <math>m + n</math>.9 KB (1,536 words) - 23:46, 25 August 2023
- But wait! We can use the rule <math>\log_b{x^y} = y*\log_b{x}</math>. Then the expression becomes This time, we can make use of the <math>\log</math> addition rule <math>\log_b{x*y} = \log_b{x}+\log_b{y}</math>. The expression becomes10 KB (1,595 words) - 21:13, 20 September 2021
- ...h>, and therefore <math>5^6 + 1 \equiv 2 \pmod 4</math>. Hence the largest power of <math>2</math> that divides <math>5^6+1</math> is <math>2^1</math>, and ...our exponent of <math>2</math> is at <math>7</math>. But the divisibility rule for <math>4</math> is the last <math>2</math> digits of the number must be7 KB (1,201 words) - 15:17, 13 November 2024
- ...h the terms are written, and indeed often list them in descending order of power. So we would write: ...andard. (Although the classical concept of a function as a "deterministic rule to compute an output based on an input" has survived in [[constructive math12 KB (2,010 words) - 23:10, 2 August 2020
- '''Sum Rule:''' [[Product Rule]]:2 KB (309 words) - 09:50, 4 June 2024
- ====General Rule==== ====General Rule====5 KB (714 words) - 16:48, 12 June 2020
- In cases where the two selectors are not identical, which rule applies depends on specificity. The full rules for determining specificity ...the most preferred style, although white-on-black (reverse video) can save power on the reader's computer, depending on the display technology. Don't make a5 KB (846 words) - 21:23, 13 July 2022
- ...o determine the number of positive and negative roots of a polynomial. The rule gives an upper bound on the number of positive or negative roots, but does ...ts is the number of sign changes after multiplying the coefficients of odd-power terms by −1, or fewer than that by a positive even number.942 bytes (147 words) - 09:44, 20 September 2016
- .... Because <math>P</math> is the midpoint of <math>AM</math>, the cotangent rule applied on triangle <math>MBA</math> gives us Hence, by the cotangent rule on <math>ABC</math>, we have13 KB (1,811 words) - 13:36, 1 June 2024
- First two integrals easily done by power rule12 KB (1,981 words) - 17:33, 3 September 2023