Mathematics 31B Practice Midterm 2 Exam Date November 16 2012 Instructor D E Weisbart NAME please print legibly Your University ID Number Your Discussion Section and TA Signature There are SEVEN questions on this examination Calculators notes and books may not be used in this examination You may not receive full credit for a correct answer if insufficient work is shown QUESTION VALUE SCORE 1 10 2 10 3 10 4 10 5 10 6 10 7 10 TOTAL 70 1 1 10 points Compute the following limits a lim x x2 1 x Answer b lim x2 1 ln x x 1 Answer 2 2 10 points a Z 4 sec3 x dx 0 Answer b Z sin 2x cos2 3x dx Answer 3 3 10 points a Z 1 2 1 x2 dx 0 Answer b Z csc 1 x dx Answer 4 4 10 points a Is the following integral convergent or divergent Z 1 x dx 4 1 x Answer b Compute Z 2 x dx 2 x 1 1 Answer 5 5 10 points a Use the midpoint rule to estimate the value of equal to 5 R2 0 cos x2 dx with the number of intervals Answer b Use any approximation method you wish to estimate 1 intervals are fine enough so that the error is less than 20 R1 0 3 x 2 dx and make sure that the Answer 6 6 10 points a Calculate the following antiderivative Z x 1 dx 2x 1 3x 1 2 Answer b Calculate the following antiderivative Z dx 2 x 1 x2 x 3 Answer 7 7 10 points a Calculate the arc lengh of the curve given by the graph y x2 where 0 x 2 Answer b An object is thrown from ground level on a flat landscape into the air with a horizontal feet feet velocity of 2 second and a vertical velocity of 32 second The acceleration due to the force of feet gravity is 32 second2 When the object hits the ground what is the length of the arc that the object traveled Answer 8