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Week1_Old test

# Week1_Old test - Mech 221 Math Problems from Old Tests...

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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 ) | &amp;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 &amp;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 &amp;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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Week1_Old test - Mech 221 Math Problems from Old Tests...

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