Math_122_200702_Exam1_solution_key

Math_122_200702_Exam1_solution_key - in sigma notation with...

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1 of 6 Exam One MATH 122 Winter, 2008 Name_______________________________ Section____________ Show all your work on the exam paper, legibly and in detail, to receive full credit. No Calculators. Some useful formulas: () ( )( ) ( ) 2 1 3 1 2 1 2 1 ; 6 1 2 1 ; 2 1 = = = + = + + = + = n k n k n k n n k n n n k n n k 1. (5 points) Given the following differentiation formula, state its corresponding integration formula. [] 2 2 1 1 x x x dx d + = + 2. (5 points) Show that the following integration formula is correct. () () () + = C x x x dx x x cos sin sin
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2 of 6 3. (5 points each) Evaluate the following definite integrals using formulas from geometry. () dx x 2 1 1 ( ) dx x x + 4 0 2 16 4. (5 points) Given the function () () = x dt t x f 0 2 cos , find ( ) 0 f and () 0 f . 5.
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3 of 6 (5points) Write the expression 11 9 7 5 3 1 + + in sigma notation with the starting value of the index of summation beginning at zero. Do not evaluate the expression. 6. (5 points) Write the expression 11 9 7 5 3 1 + +
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Unformatted text preview: in sigma notation with the starting value of the index of summation beginning at one. Do not evaluate the expression. 7. (8 Points) Evaluate the summation ( ) = 10 1 2 1 j j . 8. 4 of 6 (7 points each) Evaluate the following indefinite integrals. dx e x x 3 2 2 ( ) dx x x 2 2 sec dt t t + 12 7 2 9. 5 of 6 (12 points each) Evaluate the following definite integrals dx e e x x + 3 ln 3 ln 4 dx x + 1 2 1 10. 6 of 6 The Riemann Sum n n k n k n 3 3 1 lim 2 1 = + represents the net signed area under a curve ( ) x f on an interval [ ] b a , . (5 points) For what function and on what interval is this the Riemann Sum? (7 points) Find the net signed area that the Riemann Sum represents, using the fundamental theorem of calculus....
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Math_122_200702_Exam1_solution_key - in sigma notation with...

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