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In which quadrant do the following points lie? What is the radius of the circle with equation. The equation f. What kind of symmetry does the graph have if f. Exercises 1. Download full file from buklibry. Determine the one-sided limits of the function f. Does either of the two oscillating functions in Figure 7 appear to approach a limit as x! The values of the function graphed in B seem to settle to 0 as x! In Exercises 55—60, plot the function and use the graph to estimate the value of the limit.
Apply the method of Example 6 to f. Use a graph of f. The figures shown below illustrate why this procedure works. For each graph in Figure 7, determine whether f 0. By logarithmic differentiation xC1 2 y0 1 2x 1 D C 2 ; y x x C1 2.
Then, f 0. As x increases through 2, f. On the other hand, as x increases through 2, f 0. Then xC1 x. Note that x D 1 is not a critical point because it is not in the domain of f. As x increases through 2, f 0. As x increases through 0, f 0. Though f 0. As x increases through 1, f 0. On the other hand, as x increases through 1, f 0. Find the area of the region enclosed by the graphs of f.
For the endpoint x D 2 e 1, the series becomes. Thus, the series e. For the endpoint x D 3, the series becomes X1 X1 1 1 2 , which converges by the Limit Comparison Test comparing with the convergent p-series.
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