Given the function $\displaystyle f(x)= \frac{1}{x}$ (in blue), consider the functions $g$ (in green) and $h$ (in red) graphed below which are continuous on $(0, \infty)$. Assuming the graphs continue in the same way as $x$ goes to infinity, answer the following questions.

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choose one Converge Diverge Not sufficient information 1. Does the improper integral $\displaystyle \int_1^{\infty} f(x)\,dx$ converge, diverge, or not sufficient information?

choose one Converge Diverge Not sufficient information 2. Does the improper integral $\displaystyle \int_1^{\infty} g(x)\,dx$ converge, diverge, or not sufficient information?

choose one Converge Diverge Not sufficient information 3. Does the improper integral $\displaystyle \int_1^{\infty} h(x)\,dx$ converge, diverge, or not sufficient information?

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Note: You can click on the graph to enlarge the image.

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Note: You only have two attempts at this problem.

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