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### 2018/2019 - Topics for the Calculus I Final Exam

posted Dec 20, 2018, 4:36 PM by Matthew Grenfell   [ updated May 14, 2019, 4:22 AM ]
 Use various techniques to evaluate limits, including algebraic manipulation, graphs, and tables of values Use limit laws to evaluate limits, including sums and products of limits Use the definition of continuity to determine if a function is continuous at a point or to determine ways to make a function continuous at a point Understand and describe discontinuities on a graph Evaluate limits at infinity and determine equations of horizontal asymptotes Understand the definition of a derivative as a limit of a difference quotient Interpret the derivative at a point on a graph and use the derivative of a function to determine the equation of a tangent line at a given x-value Determine the derivative of various functions using the general power rule, product rule, quotient rule, chain rule, etc. Compute derivatives of exponential, logarithmic, and trigonometric functions Compute derivatives using implicit differentiation and logarithmic differentiation Use the concept of related rates to determine the rate of change of related variables or quantities Determine the critical numbers (x-values) of a function Use the Extreme Value Theorem to determine the absolute maximum and minimum values of a function on an interval Use properties of the first and second derivatives of a function to algebraically or geometrically determine critical numbers, intervals where the function is increasing or decreasing, intervals where the function is concave up or down, the shape of the graph, etc. Use L'Hospital's Rule to evaluate limits and determine when a limit has indeterminate form Use calculus to solve optimization problems involving an unknown quantity and a constraint Use Riemann sums to approximate the area under a curve or to approximate the value of a definite integral Evaluate definite integrals using the Fundamental Theorem of Calculus Use an appropriate substitution to evaluate definite integrals when needed Determine the area between two curves Determine the volume of a solid of revolution using the method of disks/washers Evaluating limits and using the limit laws Determine the derivative of various functions using the general power rule, product rule, quotient rule, chain rule, etc. Compute derivatives of exponential, logarithmic, and trigonometric functions Compute derivatives using implicit differentiation and logarithmic differentiation Derivatives of inverse trigonometric functions (particularly arctangent, which is most useful) Exponential growth and decay models (population growth, half-life decay, Newton's law of cooling) Sketching the graph of a function using information about the function, the first derivative, and the second derivative Evaluate definite integrals using the Fundamental Theorem of Calculus Determine antiderivatives and indefinite integrals Use an appropriate substitution to evaluate definite integrals when needed