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
(2sided) 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 .