Mathematics 134 -- Intensive Calculus for Science 2

Quiz 1

January 23, 2002

The first regular quiz of the semester will be given during the first 20 minutes of class on Friday, January 25. It will cover the material from sections 5.1 - 5.4 that we have discussed since the start of the semester. You may use a calculator on this quiz. The specific topics to be covered will be:

• Riemann sums for a function f(x) on a <= x < = b: determining Delta x from the number n of subdivisions and vice versa, computing the left- and right-hand sums from a formula, a table, or a graph for the function.
• The definite integral = limit of Riemann sums as n goes to infinity.
• The relation
  
  |RHS - LHS| = |f(b) - f(a)| Delta x
  
  and how that can be used to get estimates of integrals accurate to within a given amount.
• First applications of definite integrals:
  1. Computing the total change of a function over some range of values of the variable, given the rate of change of that function (example: given a graph/table/formula for a velocity, compute the total distance traveled over some time interval)
  2. Computing areas between graphs and the x-axis. The definite integral gives (area above axis) - (area below axis). The questions I could ask here would involve simple graphs (say made up of parts of straight lines, circles, etc.) where you would have some basic way to compute the area.
  3. Computing the average value of a function f(x) over a range of values of the variable.
     
     Average value = 1/(b-a) Integral_a^b f(x) dx
     
     

On the quiz, there will be two questions similar to problems from the problem assignments from weeks 1 and 2.

Good Review Problems