unbounded 上界:upper bound 最小上界:least upper bound 最大下界:greatest lower bound 有限区间:finite interval 无穷区 间:infinite interval 有界集:bounded set 实数系:real-number system 趋近:approach 收敛:converge 一致收敛:converge uniformly 判别法: criterion 等价:be equivalent to 逐次的:succes...
Finding 21/6 is equivalent to solving the equation f(x) = x6 - 2 = 0 Taking the derivative of f(x): f'(x) = 6x5 The recursion formula becomes: xn+1 = xn - ( xn6 - 2) / 6xn 5 . Using an initial guess of x1 = 1, we can generate the sequence of approximate ...
Check. 9(-5/2)+3≟7(-5/2)-2 Replacexby−5/2. Check. −45/2+3≟−35/2-2 Simplify. Check. −45/2+6/2≟−35/2-4/2 Change to equivalent fractions with a common denominator. ...
Always remember to remove any common factors as the first step, if it is possible to do so. EXAMPLE 4 Simplify. (9x-x^3)/(x^3+x^2-6x)= (x(9-x^2))/(x(x^2+x-6)) Remove a common factor from the polynomial in the numerator and in the denominator.= (x(3+x)(3-x))/(...
The simplest way to factor a term is to find the essential multiplication that gave origin to it. For example, to find the common factor of the expression 2x + 6x, one can break each term down: 2x = 2*x 6x = 3*2*x Observing the products, it is clear that 2x is the common...
We also give an equivalent description of convergence in D(E) with respect to the topology M1: Lemma 4.6 With respect to M1, we have ξn→ξ if and only if the following two statements hold simultaneously: (M1) Let t∉disc(ξ) . If tn→t, then ξn(tn)→ξ(t). (M2) Let t...
How can we change an equation to another equation that is equivalent to it? The answer to the first question is found by using the substitution principle. Example 13Are 5x + 2 = 6x - 1 and x = 3 equivalent equations? Solution
Equations Aquadraticequationisanequationequivalenttooneoftheform axbxc0 2 Wherea,b,andcarerealnumbersanda0 Soifwehaveanequationinxandthehighestpoweris2,itisquadratic.Tosolveaquadraticequationwegetitintheformaboveandseeifitwillfactor.x5x6 2 Getformabovebysubtracting5xandadding6toboth...
Two systems of equations are said to be equivalent if they have the same variables. a. True b. False Consider ='false' y' + (3x + 2) y^2 = 0 . Find its general solution. Show steps of derivation. Check your answer by substitution y and y' into the equation. ...
Sometimesanexpressionisrewritteninanequivalentform.3x+5+2x–6=5x–1 Thisisanexampleofanidentity.Anidentityistrueforallvaluesofx.Thisissometimeswrittenwiththesymbol≡as,3x+5+2x–6≡5x–1 Isidenticallyequalto 3of29 ©BoardworksLtd2005 Equations Anequationlinksanalgebraicexpressionandanumber,ortwoalgebraic...