![]() ![]() These are for current course guidelines only. find the slope of a line tangent to the graph of a polar equation at a point ( r, ?).sketch the graph of a polar equation r = f(?), and be able to find intercepts and points of intersection.sketch graphs of parametric equations and find the slope of a line tangent to the graph at a specified point.use parametric forms to determine first and second derivatives of a function.be able to convert between parametric and Cartesian forms for simple cases.recognise and apply the Mean Value Theorem and the Intermediate Value Theorem.compute simple antiderivatives, and apply to velocity and acceleration.sketch graphs of functions including rational, trigonometric, logarithmic and exponential functions, identifying intercepts, asymptotes, extrema, intervals of increase and decrease, and concavity.interpret and solve optimisation problems.apply derivatives to solve problems in velocity and acceleration, related rates, and functional extrema.use differentials to estimate the value of a function in the neighbourhood of a given point, and to estimate errors.apply the above differentiation methods to problems involving implicit functions, curve sketching, applied extrema, related rates, and growth and decay problems.differentiate functions by logarithmic differentiation.differentiate algebraic, trigonometric and inverse trigonometric functions as well as exponential and logarithmic functions of any base using differentiation formulas and the chain rule.calculate a derivative from the definition.determine intervals of continuity for a given function.apply L'Hôpital's rule to evaluating limits of the types: 0/0, 8/8, 8 - 8, 0 0, 8 0, 1 8.calculate infinite limits and limits at infinity.find limits involving algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions by inspection as well as by limit laws.The four-semester sequence of MATH 1120, 1220, 2321, and 2421 provides the foundation for continued studies in science, engineering, computer science, or a major in mathematics.Īt the conclusion of this course, the student should be able to: a proof of L'Hôpital's rule for the case of "0/0".proofs of the differentiation formulas for trigonometric functions from the definition of derivative. ![]() proofs of the rules of differentiation (differentiation formulas) for algebraic functions.application of the absolute value and greatest integer functions.a formal limit proof (using epsilonics).Optional Topics (included at the discretion of the instructor).definitions and relationships between polar and Cartesian coordinates.derivatives and tangent lines of functions in parametric form.parametric representation of curves in R².Parametric Equations and Polar Coordinates.asymptotic behaviour limits at infinity infinite limits.limits involving combinations of exponential, logarithmic, trigonometric, and inverse trigonometric functions.differentiation of inverse trigonometric functions.differentiation of logarithmic and exponential functions (any base).Inverse Functions: Exponential, Logarithmic and Inverse Trigonometric Functions.the differential and differential approximations.essential and removable discontinuities.continuity at a point and on an interval.
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