Math 181 Name: key

Quiz 2 June 11, 2013

You must show all work to receive credit!

All decimal approximations should be accurate to at least 4 decimal places

1.       The point P(2, ) lies on the curve .

If Q is the point on the graph with the x value given below, what is the slope of the secant line PQ?

a.       x=1

Q is the point (1,1), so the slope is


b.      x=1.9

The slope is


c.       x=1.995

The slope is



2.       Evaluate the following limits, if they exist:

a.       (evaluate numerically, showing your work)








From these points, the limit seems to be -

Confirming for x values from the other side:








These too appears to be approaching - , so that is our (2-sided) limit

b.      for the graph shown:





3.       Use the Intermediate Value Theorem to show that there is a root of the equation in the interval (1,2).


When x=1, , and when x=2, . Since is a polynomial, it is continuous, and so by the IVT it must taken on every value between -1 and 15 between x=1 and x=2. In particular, somewhere between x=1 and x=2 is a point where .