Recall that our discussion of the function log(x) was motivated by the interest in having a function f with f'(x) = 1/x. Continuing this line of reasoning, let fo(x) = log(x) and suppose that for integers n ≥ 1, we would like to have functions fn with (fn)' = fn-1. It turns out that fn can be expressed in term of polynomials and logarithms, i.e., no new functions are required. (i) Find an expression for fn. (ii) Show that the polynomial part of fn has degree n. Determine the leading coefficient Cn. Hint: The n-th harmonic number is defined by 1 1 H₂ = 1 + + + n 2 3 + 1 n

Recall that our discussion of the function log(x) was motivated by the interest in having a function f with f'(x) = 1/x. Continuing this line of reasoning, let fo(x) = log(x) and suppose that for integers n ≥ 1, we would like to have functions fn with (fn)' = fn-1. It turns out that fn can be expressed in term of polynomials and logarithms, i.e., no new functions are required. (i) Find an expression for fn. (ii) Show that the polynomial part of fn has degree n. Determine the leading coefficient Cn. Hint: The n-th harmonic number is defined by 1 1 H₂ = 1 + + + n 2 3 + 1 n

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 60SE: Use the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its...

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