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    Simplification of Product Rule: dy/dx = x^2 [6(2x + 1)^2] + (2x + 1)^3 (2x)

    Hi all, I'm learning the rules of differentiation, specifically the product rule. I understand the steps to obtain an answer, but am stuck when it comes to simplifying and taking out a common factor. For example, the answer to one of the problems is: dy/dx = x2[6(2x + 1)2] + (2x + 1)3(2x) I...
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    Algebraic fractions: Question e: 5/[x (x + 1)] - 2/x + 3/(x + 1)

    Question: . . . . .\mbox{(e) }\, \dfrac{5}{x\, (x\, +\, 1)}\, -\, \dfrac{2}{x}\, +\, \dfrac{3}{x\, +\, 1} I'm getting myself confused with this one. 1) I multiplied all the denominators, so they all became x(x+1)x(x+1). 2) Then 5x(x+1) - 2x(x+1)(x+1) + 3x(x+1)x 3) Becomes, 5x2 + 5x - 2x3 -...
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    Investment+Revenue to NPV question using a discount rate of 4%, compounded annually

    Q. During the next 3 years, a business decides to invest £10,000, at the beginning of each year. The revenue at the end of each year is: Year 1 = £5,000 Year 2 = £20,000 Year 3 = £50,000 Calculate the NPV using a discount rate of 4%, compounded annually. A. My answer was £39,997.85...
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    Geometric series with continuous compounding (deposits into sinking fund)

    Hi all, Q. A regular savings of $500 is made into a sinking fund at the start of each year for 10 years. Determine the value of the fund at the end of the tenth year on the assumption that the rate of interest is 10% compounded continuously. This is part b) of the question. I previously...
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    Geometric progression formula confusion with 100(1.01)(1.01n-1/1.01-1)

    Morning/afternoon/evening all, I'm aware of the formula: a(rn-1/r-1). However, for the following: 100(1.01)(1.01n-1/1.01-1) Apparently (Mathematics for Economics and Business - Ian Jacques), this is the same as: 10,100(1.01n-1) Is that correct? I can't find out how to get to this...
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    Supply and Demand equations are P = -5Q + 80 and P = 2Q + 10

    Hi all, Trying to solve the following problem from Mathematics for Economics and Business by Ian Jacques - Supply and Demand Analysis. The demand and supply functions of a good are given by P = -5Q + 80 P = 2Q + 10 For this first part I've already worked out the equilibrium price and quantity...
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    Another arithmetic sum series

    Question: The first term of an arithmetic series is 16 (a). The 30th term (n) is 100. Calculate S30. So again, I have the formula: Sn=n/2[2(a)+(n-1)d]. Using the data above: S30=30/2[2(16)+(30-1)d] S30=30/2[32+29d] Again, I don't understand my next step, or maybe my initial steps are...
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    Arithmetic series sum

    Hello all, would really appreciate your assistance with the following: Question: The sum of an arithmetic series is 270. The common difference is 1 and the first term is 4. Calculate the number of terms in the series. Formula: S20 = n/2(2a+(n-1)d Where: n = number of terms, a is the first...
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    Please help me here - present value / yield to maturity question

    Hi all, I would be very grateful for some help with the following question: If the interest rate is 6.5%, what is the PV of a security that pays $1,100 next year, $1,200 three year from now and $1,400 six year from now. If this security sold for $10,500, is the yield to maturity greater or less...
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