Question: Show your work in answering the questions below.

1. What is the tangent line approximation to \(\frac{1}{(1+x)^{k}}\) near \(x=0\) ?
2. Someone claims that the square root of \(\frac{1}{2}\) is about 0.5. Use (a) to explain whether this estimate is about right.
3. For which values of \(k\) is the approximation obtained in (a) larger than the actual value of \(\frac{1}{(1+x)^{k}} ?\) For which is it smaller?

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