BC 1-2
Quiz #1
Name:_________________
No Calculator for these problems.
Skills:
1 (5 pts). If the function below is a displacement curve, sketch the velocity curve on the
same set of axes.
2(5 pts). If the function below is a velocity curve, sketch the displacement curve on the
same set of axes.
3(3 pts each). Evaluate the following limits (show enough work so that I can recreate
your solution):
a.
 2 x 2  3x  9 
lim 

2
x 3 
 x  9 
3
3

2( x  h) 2 x
b. lim
h0
h
c.
 x  2.3
lim 
(Remember that  x  = largest integer less than or equal to x)
x 2
x2
2
on [1, 7]. Using step size = 2, construct both of the graph y and the
x
graph of the piece-wise defined function that approximates y . Show your scale
clearly.
4. Let y  

yappox









Using Euler’s method find a piecewise
linear approximation of y on [1,7] given
that y (1)  3 . Mark coordinates of the
endpoints of each segment clearly.
yappox









From your work above, give an estimate of y(3).
Is your estimate larger or smaller than the actual value of y(3)? Explain carefully.
Concepts:
5. Suppose that f ( x)  cos( x) sin(2 x) , sketch the graph of f given that f (0)  0 .
6. Decide with explanation whether it is possible to have a concave up function defined on
the real numbers with range (0,1) .