Consider the family of functions of the form fn(x) = logn (17) for which ZER, r...

  

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Consider the family of functions of the form fn(x) = logn (17) for which ZER, r < 1 and n > 1. a On a set of axes like the one shown below, sketch the graph of y=f2(1), y = f3(z), and y = f4(2). b Find f(x) and f(x). c Show that f" (1) = 2 (In 2)(1-z) 3 3 3 2 d Hence, or otherwise, find the Maclaurin series for f2(2), in the simplest form, up to and including the term. e Show that the Maclaurin series for f3(x), in the simplest form, up to and including the term is f3(x)= 3+ -7- + 1 In 3 2 In 3 + fi Write an expression for the Maclaurin series for 3 In 3 fn (x) = logn (17) ii Hence, show that the Maclaurin series for fe(z) = ln(7) is fe(1)= 1+1+1 + .... Consider the family of functions of the form fn(x) = logn (17) for which ZER, r < 1 and n > 1. a On a set of axes like the one shown below, sketch the graph of y=f2(1), y = f3(z), and y = f4(2). b Find f(x) and f(x). c Show that f" (1) = 2 (In 2)(1-z) 3 3 3 2 d Hence, or otherwise, find the Maclaurin series for f2(2), in the simplest form, up to and including the term. e Show that the Maclaurin series for f3(x), in the simplest form, up to and including the term is f3(x)= 3+ -7- + 1 In 3 2 In 3 + fi Write an expression for the Maclaurin series for 3 In 3 fn (x) = logn (17) ii Hence, show that the Maclaurin series for fe(z) = ln(7) is fe(1)= 1+1+1 + ....

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The provided images show two parts of a question The first part of the question defines a family of functions fnx logn leftfrac11x ight and asks for v... View the full answer