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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 positi
    6 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 c
    15 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> is
    3 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 the
    3 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 div
    7 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 becomes
    10 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 be
    7 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 math
    12 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 a
    5 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 have
    13 KB (1,811 words) - 13:36, 1 June 2024
  • First two integrals easily done by power rule
    12 KB (1,981 words) - 17:33, 3 September 2023

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