Calculus I (MA 111), Fall Quarter, 2000-2001
Quiz 1 — Thursday, September 7, 2000
Box
NAME
5 pts 1. Find the equation of the line through the two points (1, 3) and (−2, 1). Put your answer in
the y = mx + b format.
5 pts 2. Write and equation of the line through the point (−3, 2) and perpendicular to the line
x + y = 7. Again put your answer in the y = mx + b form.
5 pts 3. Is y a function of x if x2 + y 2 = 4? After saying “yes” or “no”, give a reason.
5 pts 4. Let f (x) = x1 and g(x) = x2 + 1. Find f ◦ g and g ◦ f. Show that they are not the same by
evaluating at some value of x.
−
→
−
→ →
−
→ −
→
−
→
→
→
9 pts 5. Let −
u = i +2 j , −
v = −2 i − j , and −
w =3 i .
a) Plot the three vectors on the set of axes
→
→
(b) 2−
u − 3−
v =
→
(c) −
u=
→
(d) a unit vector in the same direction as −
u is
→
(e) a unit vector in the opposite direction of −
w is
→
(f) a vector in the same direction as −
u with length 2 is
(g) Þnd a unit vector with positive components such that the angle between the vector and
−
→
w is 45 degrees.
−
→
3 pts 6. The initial and terminal points of a vector A are (−1, −2) and (3, 1), respectively. Sketch
the given directed line segment, write the vector in component form, and sketch the vector
with its initial point at the origin.
−
→
A =
8 pts 7. Give the Maple commands (and correct syntax) for the following (you may use more than
one command per question if necessary).
(a) Sketch the graph of y = 2x + 1 for x between −2 and 4.
(b) Find the solutions to the equation x2 − 3x + 1 = 0.
(c) Sketch the graphs of y = x2 and y = −2x2 + 1 for −1 x 3 on the same set of axes.
Show how to do this in two different ways.
(i)
(ii)