MATH 121 – Final Exam Study Guide
5/8/08
Material covered after Test #3:
Section 4.2
 Know Thm 3.
 Set up a Riemann sum to approximate an integral using the Right-Hand Rule.
 Use the Riemann sum definition (Thm. 4) to compute the definite integral of a quadratic
function. This would be similar to Example 2. (Formulas 5-7 on p. 209 will be provided.)
 Know Properties of Integrals 1 through 8 on pp. 213 & 214.
Section 4.3
 Know indefinite integrals on p. 220.
 Compute areas beneath a curve (i.e., definite integrals) using the Evaluation Theorem.
 Interpret Net Change Theorem as it applies to integrating a velocity function. (i.e., integrating
velocity over an interval provides the change in distance, since distance is the antiderivative of
velocity)
Section 4.4
 Know the Fundamental Theorem of Calculus (FTC), Parts I and II
 What do FTC, Parts I and II say about the relationship between differentiation and integration?
 Compute the mean (i.e., average) value of a function on an interval [a, b] and determine at what
point in the interval the function attains its average value. (pp. 232 and 233)
Section 4.5
 Compute indefinite and definite integrals using the method of u-substitution.
Section 5.1
 Know definition of inverse function and how to compute it from the original function.
 Know graphical relationship of a function and its inverse.
 Know how to compute the derivative of f-1(x) at x=a by using the derivative of f(x) at x=b, where
f(b)=a and f-1(a)=b. (p. 251)
Section 5.2
 Know the integral definition of ln x.
 Know the three Laws of Logarithms.
 Compute derivatives of functions involving ln x.
 Know (or be able to compute) antiderivatives of tan x and cot x
 Use the technique of logarithmic differentiation.
Sections 5.3 & 5.4
 Know the formal definitions of the natural exponential function f(x) = ex (i.e., it is the inverse of
ln x) and a general exponential g(x) = ax (i.e., ax = e a ln x )
 Prove d/dx ex = ex (p. 265)
 Compute derivatives and integrals involving ex, ax and logax
 Know the general shapes of exponential and logarithmic functions
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For cumulative material refer to the Study Guides for Tests #1-3 (available on the course web page)
Section 1.6 (all)
Sections 2.1 through 2.6 (all)
Section 2.8 (first two items only on linearization)
Section 3.1 (all)
Section 3.2 (Mean Value Theorem only)
Section 3.3 (all)
Section 3.4 (all)
Section 3.5 (all)
Section 3.7 (all)