T 69. Which is bigger, 7 or e™? Calculators have taken some of the mystery out of this once-challenging question. (Go ahead and check; you will see that it is a surprisingly close call.) You can answer the question without a calculator, though. a. Find an equation for the line through the origin tangent to the graph of y = In x. [-3, 6] by [–3, 3] b. Give an argument based on the graphs of y = ln x and the tangent line to explain why In x < x/e for all positive x + e. c. Show that In (xª) < x for all positive x e. d. Conclude that xº < e* for all positive x # e. e. So which is bigger, º or e™?

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