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1. Volume by washer method 3. Derivatives of tower functions (Ex: f(x)=x(2x)), derivatives involving In and e with chain rule and other rules from Calc
1. Volume by washer method 3. Derivatives of tower functions (Ex: f(x)=x"(2x)), derivatives involving In and e with chain rule and other rules from Calc | 4. Integrals involving a mixture of the following: Exponential functions with general bases or e, Natural log (In) functions, U-substitution, Algebraic approaches: multiplying by a convenient form of 1, subtle substitution, splitting up fractions, long division, completing the square, Integration by parts (with or without evaluation), Trig integrals (powers of sin and cos), Trig substitution, Partial fraction decomposition, Improper integrals 5. Sequences: Find a recurrence relation that generates the sequence and an explicit formula for the nth term of the sequence 6. Series: Convergence/Divergence: Divergence test, Integral test, p-series test, Comparison and Limit Comparison tests, Alternating series test, Ratio and Root tests, Absolute and Conditional convergence. In particular: a. A series that converges and you can evaluate: geometric (identify and use the formula) and/or telescoping (nd formula for the nth term of the sequence of partial sums and then take the limit to nd the value of the sequence) b. A series that when written as a function can be integrated (Integral test), this is where I will test improper integrals c. A series involving k! and kAk: Ratio or Root test d. A series that when written as a function is a rational function: Comparison and/or Limit Comparison test e. An Alternating Series 7. Power Series: interval and radius of convergence 8. Taylor Series, Maclaurin series, Binomial series
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