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# (a) If $g(x) = \frac{1}{(\sqrt{x} - 1)}$, use your calculator or computer to make a table of approximate values of $\displaystyle \int_2^t g(x)\ dx$ for $t = 5, 10, 100, 1000$, and $10,000$. Does it appear that $\displaystyle \int_2^\infty g(x)\ dx$ is convergent or divergent?(b) Use the Comparison Theorem with $f(x) = \frac{1}{\sqrt{x}}$ to show that $\displaystyle \int_2^\infty g(x)\ dx$ is divergent.(c) Illustrate part (b) by graphing $f$ and $g$ on the same screen for $2 \le x \le 20$. Use your graph to explain intuitively why $\displaystyle \int_2^\infty g(x)\ dx$ is divergent.

## a. Divergentb. Divergentc. Divergent

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