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)

x

.5

-.48967

.1

-.49958

.002

-.4999998

From these points, the limit seems to be -

Confirming for x values from the other side:

x

-.1

-.49958

-.01

-.4999958

-.0006

-.499999985

These too appears to be approaching - , 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 .