Calculus I :: Lab 01

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1. Graph the function \(\displaystyle f(x) = \frac{e^x-1}{x}\).
2. From the graph estimate \(\displaystyle \lim_{x \to 0} f(x)\).
3. Make a table with two columns and at least five rows. One column should show \(\displaystyle x \to 0^-\) and the other column should show the corresponding \(\displaystyle f(x)\) values.
4. Make a table with two columns and at least five rows. One column should show \(\displaystyle x \to 0^+\) and the other column should show the corresponding \(\displaystyle f(x)\) values.
5. Using the tables, estimate \(\displaystyle \lim_{x\to 0} f(x)\).

1. Graph the function \(\displaystyle g(x) = \frac{\sqrt{x}-1}{x-1}\).
2. From your graph, estimate \(\displaystyle \lim_{x\to 1} g(x)\).
3. Make two tables as you did in Problem 1, one should show the limit from the left, and one should show the limit from the right.
4. Do your tables agree with your previous estimate? If not make a new estimate.
5. Add a slider for the variable \(b\). Show the value of \(g(b)\) and the point \(b,g(b)\).

1. Graph the function \(\displaystyle h(x) = \frac{\cos(x) -1}{x}\).
2. From your graph, estimate \(\displaystyle \lim_{x\to 0} h(x)\).
3. Make two tables as you did in Problem 1, one should show the limit from the left, and one should show the limit from the right.
4. Do your tables agree with your previous estimate? If not make a new estimate.
5. Add a slider for the variable \(c\). Show the value of \(h(c)\) and the point \(c,h(c)\).

1. You are given the graph of an unknown function \(\displaystyle k(x)\). From the graph estimate \(\displaystyle \lim_{x \to \pi/2} k(x)\).
2. Make tables to further estimate \(\displaystyle \lim_{x \to \pi/2} k(x)\).
3. Add a slider as you have done before.

1. You are given two tables of an unknown function.
2. From these tables estimate the limit of the function as \(x \to 0\).
3. Graph the function \(j(x)\). Does the graph agree with your estimation? Why or why not?

Here is an example of what your solution might look like. Be creative and professional in your work.