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writing sin3a.cos3a = sin3a.cos2a.cosa= sin3a.(1-sin2a).cosaput sin a as then cos a da = dt integral(t3(1-t2).dt= integral of t3- t5 dt= t4/4-t6/6 + c where t = sina
Fundamental Theorem of Calculus, Part II Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =
find the ratio of each of the following in simplest form 1] 9 months to 7 by 4
Rates of Change or instantaneous rate of change ; Now we need to look at is the rate of change problem. It will turn out to be one of the most significant concepts . We will c
Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
If α,β are the zeros of the polynomial 2x 2 - 4x + 5 find the value of a) α 2 + β 2 b) (α - β) 2 . Ans : p (x) = 2 x 2 - 4 x + 5 (Ans: a) -1 , b) -6) α + β =
Teng is designing a house and in each room he can choose from tiles, floorboards, or carpet for the floor. a. How many combinations of flooring materials are possible if he designs
Q. What is Factorial? A factorial is a number with a factorial sign, !, after it. 5! is read "five factorial." 3! is read "three factorial." The factorial of a natural
Sketch the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Find out how the solutions behave as t → ∞ and
In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may
Determine the domain of each of the following functions. f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by
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