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Chapter 1: Problem 56
Describe the interval(s) on which the function is continuous. $$ f(x)=\frac{x+1}{\sqrt{x}} $$
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Use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. \(\lim _{x \rightarrow-2^{-}} \frac{1}{x+2}\)
Use a graphing utility to estimate the limit (if it exists). \(\lim _{x \rightarrow-4} \frac{x^{3}+4 x^{2}+x+4}{2 x^{2}+7 x-4}\)
Find the limit (if it exists). \(\lim _{s \rightarrow 1} f(s),\) where \(f(s)=\left\\{\begin{array}{ll}{s,} & {s \leq 1} \\ {1-s,} & {s>1}\end{array}\right.\)
Use a graphing utility to graph the function on the interval \([-4,4] .\) Does the graph of the function appear to be continuous on this interval? Is the function in fact continuous on \([-4,4] ?\) Write a short paragraph about the importance of examining a function analytically as well as graphically. $$ f(x)=\frac{x^{2}+x}{x} $$
The amounts (in billions of dollars) spent on prescription drugs in the United States from 1991 through 2005 (see figure) can be approximated by the model $$ d(t)=\left\\{\begin{array}{ll}{y=0.68 t^{2}-0.3 t+45,} & {1 \leq t \leq 8} \\\ {y=16.7 t-45,} & {9 \leq t \leq 15}\end{array}\right. $$ where \(t\) represents the year, with \(t=1\) corresponding to 1991. (a) Use a graphing utility to graph the function. (b) Find the amounts spent on prescription drugs in 1997 , \(2000,\) and 2004 .
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