<p> MTH 251 EXAM II REVIEW</p><p>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.</p><p>2.7 Precise Definitions of Limits • Be able to find the d , in the definition of the limit, for a given e using the graph of a function. • Be able to find the d , in the definition of the limit, for a given e using the equation of a function. • Be able prove the existence of a limit using the e , d definition of a limit.</p><p>3.1 Introducing the Derivative • Be able to use the definitions on pages 127 and 129 to find the slope of the tangent line at a point for a function. • Be able to find the derivative of a function at a particular value of x = a. • Be able to find the equation of the tangent line to a curve at a point. • Be able to determine the function and value of x = a for a limit representing the derivative of a function.</p><p>3.2 Working with Derivatives • Be able to match the graph of a function with the graph of its derivative. • Be able to graph the derivative of a function, given a graph of the function. • Be able to graph the derivative of a function, given the equation of the function. • Be able to determine where the graph of a function is continuous/differentiable. • Be able to find the equation of the normal line to a curve at a point.</p><p>3.3 Rules of Differentiation • Be able to calculate derivatives of functions using the constant rule, power rule, constant multiple rule, sum and difference rules. • Be able to calculate derivatives of exponential functions. • Be able to find the equation of the tangent line to a function at a point. • Be able to find second and third derivatives of functions. 3.4 The Product and Quotient Rules • Be able to determine derivatives of functions using the product and quotient rules. • Be able to find the equation of the tangent line to a function at a point. • Be able to find the second derivative of a function at a point using the product and quotient rules.</p><p>3.5 Derivatives of Trigonometric Functions • Be able to determine the derivatives of all 6 of the trigonometric functions. • Be able to find the derivative of a function involving trigonometric, polynomial and exponential functions using the product and quotient rules. • Be able to find the second derivative of a function involving trigonometric functions. • Be able to find the equation of the tangent line to a function at a point. • Be able to evaluate limits involving trigonometric functions.</p><p>3.6 Derivatives as Rates of Change • Be able to solve applied problems involving velocity and acceleration. • Be able to solve applied problems involving other rates of change.</p><p>Chapter 2 Review (p. 123) 47 – 53 odd, 58, 60, 61</p><p>Chapter 3 Review (p. 232) 1, 3, 5, 6, 11 - 15, 17, 21, 41, 45, 49, 51, 54</p>