MTH 251 - CALCULUS
EXAM I REVIEW
1.1 Review of Functions
• Be able to determine whether a relation is a function.
• Be able to find domains and ranges of functions.
• Be able to graph functions.
• Be able to find the composition of two or more functions.
• Be able to evaluate the difference quotient for a function.
• Be able to determine whether a relation is symmetric to the x-axis, y-axis, or origin.
1.2 Representing Functions
• Know the four representations of a function (verbal, numerical, visual, and algebraic).
• Be able to classify functions into one of the following categories: Polynomial, Rational, Power, Root, Trigonometric, Exponential or Logarithmic.
• Be able to graph piece-wise functions.
• Be able to adjust and graph functions by stretching, shrinking, shifting them left, right, up or down.
• Be able to adjust and graph functions by reflecting them across the x or y-axis.
• Be able to add, subtract, multiply and divide two functions and determine their domains.
1.3 Inverse, Exponential and Logarithmic Functions
• Be able determine whether a function is one-to-one.
• Be able to find the inverse of a function given in tabular, graphical or algebraic form.
• Be able to solve logarithmic equations.
• Be able to solve exponential equations.
1.4 Trigonometric Functions and Their Inverses
• Be able to evaluate trigonometric functions.
• Be able to prove trigonometric identities.
• Be able to solve trigonometric equations.
• Be able to evaluate inverse trigonometric functions.
• Be able to find the value of the remaining 5 trigonometric functions, given information about the other one.
2.1 The Idea of Limits
• Be able to evaluate the slope of a secantline.
• Be able to approximate the slope of the tangent line to a curve using the slopes of secant lines.
• Be able to find the average velocity of an object over a specified time interval.
• Be able to approximate the instantaneous velocity of an object using the average velocity over a short time interval.
2.2 Definitions of Limits
• Be able to calculate limits given the graph of a function.
• Be able to calculate limits numerically using a table.
• Be able to calculate one-sided limits using a graph and table.
• Be able to sketch the graph of a function given information about any limits of the function.
2.3 Techniques of Computing Limits
• Be able to calculate limits using the Limit Laws.
• Be able to calculate limits by plugging in.
• Be able to calculate limits by factoring.
• Be able to calculate limits using conjugates.
• Be able to calculate limits using algebra.
• Be able to calculate one-sided limits.
• Be able to apply the Squeeze Theorem.
2.4 Infinite Limits: Vertical Asymptotes
• Be able to determine when a function has an infinite limit using a graph.
• Be able to determine when a function has an infinite limit using a table.
• Be able to determine when a function has an infinite limit by analyzing the expression.
• Be able to find vertical asymptotes for rational, trigonometric and logarithmic functions.
2.5 Limits at Infinity: Horizontal Asymptotes
• Be able to calculate limits at infinity for functions.
• Be able to determine when a function has an infinite limit as a limit at infinity by analyzing the expression.
• Be able to find horizontal, vertical and slant asymptotes for a function.
• Be able to find the limits at infinity for exponential, logarithmic and trigonometric functions.
• Be able to sketch the graph of functions given information about infinite limits and limits at infinity.
2.6 Continuity
• Be able to determine from a graph where a function is continuous.
• Be able to state the type of discontinuity (removable, jump or infinite) for a function at a particular value ofx.
• Be able to determine from a formula whether a function is continuous at a point.
• Be able to determine from a formula on what intervals a function is continuous.
• Be able to find the limit of a function using continuity.
• Be able to apply the Intermediate Value Theorem.
Chapter 1 Review 1, 9, 13 – 23 odd, 27, 37 – 47 odd, 51
Chapter 2 Review 1 – 13 odd, 17, 23, 25, 27, 31, 33 – 53 odd