Recent content by Gallagher

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    Finding the nth+1 derivative via Leibniz

    Homework Statement I'm told to find the nth derivative of a function via http://www.math.osu.edu/~nevai.1/H16x/DOCUMENTS/leibniz_product_formula_H6.pdf. Homework Equations Then I'm asked to show that f(n+1)=f(n)+3n(n-1)f(n-2) evaluated at x=0 when n>1 The Attempt at a Solution...
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    Understanding the Limit of Natural Log: ln(x^2-16) as x Approaches 4+

    I think it is just substituting in t for the function inside the natural log to make it easier to understand. Putting 4 into the equation you get 42-16=16-16=0 so it is the limit of ln(0). Thinking about ln(0), it is undefined as it represents the number you would need to take e to the power of...
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    Find all x such that |x-1|+|x-2|>1.

    Case 1 looks right to me. Plugging 2 in you get |2-1|+|2-2|>1 ==> 1+0>1 so x has to be at least bigger than 2.
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    Differential Equation of Two Functions

    Hi Tiny Tim! I don't think I understand your advice. As X is a constant, not a function, I don't think you could take X'. What I think you're referring to is the initial condition of f(X)=1. As such you would think that f'(X) would = 0 but, as I will show, that is not the case and f'(X)=c as...
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    Integrating 3cos[SUP]5[/SUP]3xdx

    They don't integrate sin43x into sin53x/5 but rather, they integrate sin43xcos3x into sin53x/5. Thinking about sin53x/5 this makes sense as if you were to differentiate that function you would get nfn-1 per the power rule which is sin43x times the derivative of the inner function per the...
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    Differential Equation of Two Functions

    Homework Statement f '(x)-cf(x)+g(x)=0 Homework Equations f(X)=1 f(x)=e-c(X-x) + ∫xX e-c(r-x) * g(r)dr X is a constant. The Attempt at a Solution Ok, so the part of this problem that is confusing me is the integral within the function, f(x). It is an exponential function times an unknown...
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    Normal Distribution: PDF of a Normally Distributed Random Variable

    Sir, you are a God among men. The brilliance of your statement, "As sigma has already be taken, to prevent confusion, let's call the standard deviation d", is beyond measure. You have my eternal gratitude.
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    Normal Distribution: PDF of a Normally Distributed Random Variable

    Homework Statement A Normally distributed random variable with mean μ has a probability density function given by _ρ_...*...((-ρ2(x-μ)2)/2δ) √2∏δ|...e^ Homework Equations Its standard deviation is given by: A)ρ2/δ B)δ/ρ C)√δ|/ρ D)ρ/√δ| E)√δ|/2ρ The Attempt at a Solution...