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Unformatted text preview: Statements, definitions and proofs that may appear on the second midterm. Statements: 1. State the chain rule. 2. Define what is the inverse function and what is the condition for its existence. State the formula for the derivative of inverse function. 3. State the properties of the exponential function ex . 4. State the properties of natural logarithm ln x. 5. State Rolle's theorem. 6. State Mean Value Theorem. 7. State the formulas for (sin1 ) (x), (cos1 ) (x), (tan1 ) (x) and (sec1 ) (x) Proofs: 1. Prove Rolle's theorem. You may assume that if the function f is differentiable and x0 its local maximum or minimum, then f (x0 ) = 0. 2. Prove that if x0 is a local maximum of a differentiable function f defined on some interval around x0 , then f (x0 ) = 0. 3. Prove that limh0 (1 + h)1/h = e. You can assume that the limit exists and you can use without proof all the properties of ln x that you need (but only correct ones!). 4. Derive the formula for (sin1 ) (x) (or (cos1 ) (x), (tan1 ) (x)). 1 ...
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This note was uploaded on 03/27/2008 for the course MATH 211 taught by Professor Onlineresources during the Spring '06 term at University of Wisconsin Colleges Online.
 Spring '06
 OnlineResources
 Chain Rule, Derivative, The Chain Rule

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