CalcReview - under a curve. Know how to integrate...

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STA 505 Review of Calculus Worksheet To be successful in the course, you should have a strong background in calculus. You should be familiar with techniques of differentiation and integration, infinite series, sequences, among other topics from Calculus I and II. Below you will find a more detailed explanation of what is expected, along with some practice problems. Derivatives Know the Power Rule, Chain Rule, and Product Rule. Know either the Quotient Rule or hos to combine the previous rules to get it. Know the derivatives of exponential and logarithmic functions. Know how to use the derivative to find minimums and maximums. Know how to take second derivatives. Know how to take partial derivatives. For each of the following expressions, make sure you can take both the first and second derivatives with respect to the variable x . 1. 5 x x x π + + 2. 17 x e 3. 2 3 5 x x e 4. ( 29 2 ln x 5. ( 29 ln x e 6. 5 3 14 x x - Integrals Know the Power Rule for Integrals. Know how to take definite or indefinite integrals. Know how to implement u -substitution and integration by parts. Know the conceptual definition of an integral as the area
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Unformatted text preview: under a curve. Know how to integrate exponential functions. Know how to take improper integrals. Compute the following integrals. 1. 2 5 x e dx ∫ 2. 2 3 1 5 3 x x dx + + ∫ 3. x xe dx ∫ 4. x xe dx ∞-∫ 5. ( 29 1 2 3 2 1 5 7 x y xy x y dydx = = + ∫ ∫ Geometric Series Know the basic ideas behind the convergence and divergence of infinite series. Know the rules for when geometric series converge and diverge. Do the series converge or diverge? If they converge, what do they converge to? 1. 1 1 4 i i ∞ = ∑ 2. 1 5 4 i i ∞ = ∑ 3. 1 5 4 i i ∞ = ∑ 4. What is the Taylor series expansion for x e ? Rules for Exponents and Logs Simplify if possible using exponent and logarithmic identities. 1. ( 29 ln ab 2. a b e e 3. ( 29 ln a b + 4. ( 29 3 ln x 5. ( 29 ln x e...
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This note was uploaded on 09/29/2009 for the course STA 505 taught by Professor Lisamarano during the Spring '09 term at West Chester.

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CalcReview - under a curve. Know how to integrate...

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