Solved: For 9192, define A(t) to be the arc length of thegraph of y = f(x) from x = 0 to

Chapter 8, Problem 91

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For 9192, define A(t) to be the arc length of thegraph of y = f(x) from x = 0 to x = t, for t 0.(a) Use the integral expression for arc length and a computeralgebra system to obtain a formula for A(t).(b) Graph A(t) for 0 t 10. What simple function doesA(t) look like? What does this tell you about the approximatevalue of A(t) for large t?(c) In order to estimate arc length visually, you need thesame scales on both axes, so that the lengths are not distortedin one direction. Draw a graph of f(x) with viewingwindow 0 x 100, 0 y 100. Explain whatyou noticed in part (b) in terms of this graph.f(x) = x2