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Practice Test 3b - Name 19 November 2009 Teaching Assistant...

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Name 19 November 2009 Teaching Assistant Hour Test 3 Math 1501 J Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but are by no means necessary. Pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) a. Evaluate i. ( 29 )) ln(cos( x dx d ii. ( 29 ) arccos( x x dx d b. Define the hyperbolic sine, hyperbolic cosine, and hyperbolic tangent functions by 2 ) sinh( x x e e x - - = , 2 ) cosh( x x e e x - + = , and ) cosh( ) sinh( ) tanh( x x x = . Then i. Show that ) cosh( ) sinh( x x dx d = and ) sinh( ) cosh( x x dx d = iii. Show that 1 ) ( sinh ) ( cosh 2 2 = - x x iv. Calculate the derivative of ) tanh( x 2. (25) Evaluate the integrals a. - dx e x x 2 b. e dx x x 1 ) ln( c. + 2 16 x dx x d. + 2 16 x dx
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Name Page 2 of 3 Hour Test 3 Teaching Assistant 19 November 2009 3. (25) The region sketched below is bounded by the interval [0,1] on the y -axis, the interval [ ] 2 , 0 π
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