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Final Exam Study Guide for Calculus I
Typology: Cheat Sheet
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The final exam will be a 2.5 hour CUMULATIVE exam. This means that in principle, you are responsible for everything we have covered this term. As a study aid, I have listed below the major definitions, theorems, proofs, deriva- tions, and ideas that you are responsible for. I have NOT individually listed the various differentiation formulas and techniques that we have learned: you are nevertheless responsible for them. In particular, you should be able to differentiate any function that I put in front of you, which means that you need to know (for example) the product rule, the chain rule, how to differ- entiate exponential functions, etc., etc. Moreover, you need to be able to use implicit and logarithmic differentiation if necessary. Finally, you should be able to compute derivatives and integrals directly from the definitions if asked to do so. As I mentioned in class, I good way of checking your overall comprehension of the differential calculus is to carefully practice using the DIADECIS method to sketch the graphs of functions. Since you never know ahead of time what differentiation technique you will have to use, or what limits you will need to compute, these problems will force you to review all the computational techniques that we have learned.
Definitions:
a) Provisional, intuitive versions b) Precise versions (with , δ, M, N , etc.)
Theorems:
Proofs:
a) f ′(x) = 0 for all x ∈ (a, b) implies f is constant on (a, b) b) Increasing / Decreasing Test
Derivations: