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, ½) 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)

 x .5 -.48967 .1 -.49958 .002 -.4999998

From these points, the limit seems to be -½

Confirming for x values from the other side:

 x -.1 -.49958 -.01 -.4999958 -.0006 -.499999985

These too appears to be approaching -½ , so that is our (2-sided) limit

b.      for the graph shown:

4

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 .