05spex1 - MATH 222 SPRING 2005 FIRST MIDTERM Grade 1 2 3 4...

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Unformatted text preview: MATH 222- SPRING 2005 FIRST MIDTERM Grade 1 2 3 4 MATH 222- SPRING 2005 FIRST MIDTERM (1) (25 pts) Calculate the following integrals. 1 1r /x" In 2$dx / xe$2+ 1 dr / sin 5x cos 5xdx 0 —7|’ Write the partial fraction decomposition of the following fraction and integrate it 2 + 2x x2(2+x2)' MATH 222- SPRING 2005 FIRST MIDTERM (2) (25pts) Compute the recursion formula for the integral / xneaxdx / x4e3ld1: and use it to compute Find the limit cosn lim 2 TL—‘OC TL MATH 222- SPRING 2005 FIRST MIDTERM (3) (25pts) Calculate the Taylor series for the function g(:c) = 2m cos(:r2). Be sure to give the general term of the series (the one in place n) 6'12 1—1‘2 Calculate T4f(x) for the function f(:1:) = little—oh here). (you need to use MATH 222» SPRING 2005 FIRST MlDTERM (4) (25pts) To calculate e we will use T3f(1) instead of f(1) = 6, With f(x) 2 ex. Calculate an upper bound for the error we make. Show that the function cos 12 is equal to its Taylor series. ...
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05spex1 - MATH 222 SPRING 2005 FIRST MIDTERM Grade 1 2 3 4...

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