MTH 252 - CALCULUS



MTH 251 - CALCULUS

EXAM I REVIEW

1.1 Review of Functions

• Be able to find the domain of a function.

• Be able to find the composition of two or more functions.

• Be able to evaluate the difference quotient for a function.

1.2 Representing Functions

• Know the four representations of a function (verbal, numerical, visual, and algebraic).

• 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.

1.3 Inverse, Exponential and Logarithmic Functions

• 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 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.

• Be able to graph trigonometric functions by determining the amplitude, period and any phase shifts.

2.1 The Idea of Limits

• Be able to evaluate the slope of a secant line.

• 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 oblique/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 of x.

• 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.

2.7 Precise Definitions of Limits

• Be able to find the [pic], in the definition of the limit, for a given [pic] using the graph of a function.

• Be able to find the [pic], in the definition of the limit, for a given [pic] using the equation of a function.

• Be able prove the existence of a limit using the [pic]-[pic] definition (precise definition) of a limit.

Chapter 1 Review 11, 13, 15, 19, 21, 23, 39, 43 – 51 odd, 55 – 61 odd, 65, 67, 71 – 83 odd

Chapter 2 Review 1 – 17 odd, 21, 27, 29, 33, 35, 37, 41, 51, 53 – 65 odd, 71 – 83 odd, 86, 87, 89

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