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Q: How do you solve log4 3-x -log2 x-1 0?

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Let y = 3x y' = 3(x)' y' = 3(x1)' y' = 3[1x(1-1)] y' = 3(1x0) y' = 3(1 x 1) y' = 3 In general: y = xn y' nx(n-1)

inverse matrix. x1+x2+x3=3,000 -x1+5x2=0 2x1-3x3=0.

it equals x1 it equals x1

This part is sometimes referred to as the First Fundamental Theorem of Calculus.Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b], byThen, F is continuous on [a, b], differentiable on the open interval (a, b), andfor all x in (a, b).ProofFor a given f(t), define the function F(x) asFor any two numbers x1 and x1 + Δx in [a, b], we haveandSubtracting the two equations givesIt can be shown that (The sum of the areas of two adjacent regions is equal to the area of both regions combined.)Manipulating this equation givesSubstituting the above into (1) results inAccording to the mean value theorem for integration, there exists a c in [x1, x1 + Δx] such thatSubstituting the above into (2) we getDividing both sides by Δx gives Notice that the expression on the left side of the equation is Newton's difference quotient for F at x1.Take the limit as Δx → 0 on both sides of the equation.The expression on the left side of the equation is the definition of the derivative of F at x1.To find the other limit, we will use the squeeze theorem. The number c is in the interval [x1, x1 + Δx], so x1 ≤ c ≤ x1 + Δx.Also, andTherefore, according to the squeeze theorem,Substituting into (3), we getThe function f is continuous at c, so the limit can be taken inside the function. Therefore, we get which completes the proof.

Need two points. m = slope. (X1, Y1) and (X2, Y2) m = Y2 - Y1/X2 - X1 ==============Or, if function is in this form...... Y =mX + b ======== Read off of function, or get function is this form.

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1 x1 = 13 x 6 = 18

Right, 3x-4x+9x-x1. 3x - x = 2x2. 9x-4x = 5x- 2x +5x = 7x

Points: (x1, y1) and (x2, y2) Slope: y1-y2/x1-x2

To solve derivatives of monomials, use as the general term:When f(x)=xn, f'(x)[the derivative]=nxn-1Example 1: 2x6 = 2(6)x6-1= 12x5Example 2: 3x = 3(1)x1-1=3x0=3

(3x)(x2) = 3x3.Think of this as (3x1)(1x2). First multiply the numbers: (3)(1) = 3. next multiply the variables: (x1)(x2) = x1+2 = x3 (when you multiply powers with the same base, add the exponents)

81

Although there are formal methods, the simplest is to see if the cubic can be factorised. If so, you'll have a linear factor and a quadratic, both of which are easy to solve. Alternatively, you could try solving it graphically. Another possibility is to solve it numerically. The derivative of a cubic, of the form f(x) = ax3 + bx2 + cx + d is f'(x) = 3ax2 + 2bx + c. Make an initial estimate x1. An improved estimate is x2 = x1 - f(x1)/f'(x1). Use x2 to make next estimate, and so on.

Aaron Poison/Bug x1 Bug/Fighting x1 Bug/Flying x2 Poison/Dark x1 Bertha Water/Ground x2 Ground x1 Rock x1 Rock/Ground x1 Flint Fire x1 Fire/Fighting x1 Steel/Ground x1 Normal x1 Ghost/Flying x1 Lucian Psychic x2 Normal/Psychic x1 Fight/Psychic x1 Steel/Psychic x1 Cynthia Ghost/Dark x1 Dragon/Ground x1 Water/Ground x1 Water x1 Grass/Poison x1 Steel/Fighting x1

Th e two points are X1,Y1 and X2, Y2 slope, m, is y2-y1 divided by x2-x1 then standard form is y = mx +b plug in y2 for y and x2 for x and solve b or plug in y1 for y and x1 for x and solve b

y = 6*x1/2 - 3x dy/dx = 6*(1/2)*x-1/2 - 3 = 3x-1/2 - 3 = 3/sqrt(x) - 3 or 3[1/sqrt(x) - 1]

Well I personally believe this is a well-balanced deck with really good effects.MONSTERS: Kaiser Sea Horse (x1), Gravi-Crush Dragon (x1), Dark Crusader (x2),Gemini Lancer (x1), Element Saurus (x1), Gladiator Beast Andal (x2),La Jinn The Mystical Genie of The Lamp (x1), Summoned Skull (x1), Destiny Hero-Defender (x1), Elemental Hero Neos (x1), Black Luster Soldier-Envoy of the Beginning (x1),The Six Samurai-Irou (x1), Double Coston (x1), Dark Blade (x1), The Forgiving Maiden (x1),Familiar Knight (x1), Evil Hero-Infernal Gainer (x1), Opticlops (x1), Zombrya The Dark (x1),Royal Magic Library (x1). TOTAL MONSTERS: 22SPELLS: Change of Heart (x1), Fusion Sword Murasame Blade (x1), Premature Burial (x1),Burden of The Mighty (x1), Mystic Plasma Zone (x1), Tribute to The Doomed (x1),Rush Recklessly (x1), Pot of Greed (x1), Ookazi (x1), Different Dimension Capsule (x1).TOTAL SPELLS: 10TRAPS: Gemini Trap Hole (x1), Dimensional Prison (x1), Call of The Earthbound (x1),Magic Cylinder (x1), Magic Jammer (x1), Trap Jammer (x1), Trap Hole (x1),Xing Zhen Hu (x1). TOTAL TRAPS: 8 TOTAL CARDS: 40

Ok this is my Deck... Monsters (19) Raging Flame Sprite (x1) Disciple of the Forbidden Spell (x2) Relinquished (x2) Wall of Illusion (x2) Cyber Jar (x1) Ebon Magician Curran (x1) Copycat (x2) Impachi (x1) Hane-Hane (x1) Spear Cretin (x1) Mystic Lamp (x1) Bowagain (x1) Swarm of Scarabs (x1) Magician of Faith (x1) Princess of Tsurugi (x1) White Magician Pikeru (x1) Blade Rabbit (x1) Old Vindictive Magician (x1) Magic (17) Graceful Charity (x1) Pot of Greed (x1) Magical Mallet (x1) Lightning Vortex (x1) Change of Heart (x1) Two-Man Cell Battle (x1) Premature Burial (x1) Mystical Space Typhoon (x1) Dark Hole (x1) Swords of Revealing Light (x1) Level Limit Area B (x2) Different Dimension Capsule (x1) Black Illusion Ritual (x2) Monster Reborn (x1) Traps (8) Sakurestu Armor (x2) Trap Hole (x1) Non Aggression Area (x1) Negate Attack (x1) Magic Jammer (x1) Chthonian Blast (x1) Spellbinding Circle (x1)

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