Linear Approximation Consider the function with the solution point (a) Use a graphing

Chapter 2, Problem 81

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Linear Approximation Consider the function with the solution point (a) Use a graphing utility to graph Use the feature to obtain successive magnifications of the graph in the neighborhood of the point After zooming in a few times, the graph should appear nearly linear. Use the feature to determine the coordinates of a point near Find an equation of the secant line through the two points. (b) Find the equation of the line tangent to the graph of passing through the given point. Why are the linear functions and nearly the same? (c) Use a graphing utility to graph and on the same set of coordinate axes. Note that is a good approximation of when is close to 4. What happens to the accuracy of the approximation as you move farther away from the point of tangency? (d) Demonstrate the conclusion in part (c) by completing the table. 4x