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Unformatted text preview: MAT131 Fall 2008 Final Review Sheet The final exam will be cumulative . Please look at the review sheets for Midterms 1 and 2 to review the material from earlier in the semester. (We may choose to write up a few more problems from earlier in the semester. You can find many more such problems in the textbook and on exams from previous semesters.) Particular emphasis on the final will be placed on the material which has not been tested on Midterms 1 or 2. Among this new material is the following. (i) Related rates problems. Given several dependent variables which are differentiable functions of the same independent variable, and given constraints among these dependent variables, solve for an unknown rate of change from given rates of change. Combine this with problem- solving skills to handle related rates word problems. (ii) Absolute maxima and minima; local maxima and minima; inflection points. Know how to find the absolute maximum and absolute mini- mum value of a differentiable function on a closed, bounded interval. Know how to find local maxima and minima and inflection points of functions, and use this to help graph the function. (iii) L’Hˆopital’s rule. Recognize indeterminate forms. Simplify limits lead- ing to 0 / 0 and ∞ / ∞ indeterminate forms using l’Hˆ opital’s rule. Know how to transform other indeterminate forms into one of these two types. (iv) Optimization problems. Given a word problem attempting to maximize or minimize some quantity given a collection of constraints, turn this into a calculus problem for finding an absolute maximum or absolute minimum. Solve this calculus problem. 1 (v) Antiderivatives. Recognize the most common antiderivatives: those arising as the derivatives of x n , trigonometric functions, exponential functions, logarithmic functions and inverse trigonometric functions. (vi) Know how to set up a Riemann sum associated to a given integrand and a given interval. Be able to evaluate the limit of Riemann sums to compute the Riemann integral in the case of some simple integrands....
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- Fall '08
- Calculus, lim, Riemann sum