advertisement

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)