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Unformatted text preview: Mech 221 Math Problems from Old Tests, Week #1 Brian Wetton September 20, 2010 Notes: This contains all questions on Mech 221 tests and exams from 2006 09 on the material on numerical methods from the first four lectures. Some of this material may appear on your test #2 this year, depending on how far I get in the first week of lectures. Remember that, as discussed in class, no solutions will be provided for these questions . Short Question, Test #1, 2006: Experimental measurements determine that a function f ( x ) satisfies f (0) = 1 , df dx (0) = 1 , and f (1) = 3 (a) Estimate f (1 / 2) using tangent line (linear) approximation. (b) Estimate f (1 / 2) using linear interpolation. Short Question, Test #1, 2008: Experimental measurements determine that a function f ( x ) satisfies f (0) = 0 , f (1) = 1 , and f (2) = 2 . 5 (a) Estimate R 2 f ( x ) dx using the Trapezoidal Rule. (b) If it is known that  f 00 ( x )  &lt; 4 for all x in the interval [0,2], how accurate is your answer in part (a)? Short Question,Test #2, 2008: The statements of two theorems are given below: Intermediate Value Theorem: If f is a continuous function, for any 1 pair of values a &lt; b and A between f ( a ) and f ( b ) there is a c between a and b such that f ( c ) = A . Mean Value Theorem: If f is a differentiable function, for any pair of values a &lt; b there is a d between a and b such that f ( d ) = f ( b ) f ( a ) b a (a) [2 marks] On the graph below, indicate the value...
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 Spring '10
 WETTON
 Numerical Analysis, Intermediate Value Theorem, Mean Value Theorem, Continuous function

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