Mathematics 31B - Practice Midterm 2Exam Date: November 16, 2012Instructor: D.E.WeisbartNAME (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 isshown.QUESTION VALUE SCORE1 102 103 104 105 106 107 10TOTAL 7011. (10 points) Compute the following limits.a.limx→∞√x2+ 1 − x=—————————Answerb.limx→1(x2− 1) ln(x) =—————————Answer22. (10 points)a.Zπ40sec3(x) dx =—————————Answerb.Zsin(2x) cos2(3x) dx =—————————Answer33. (10 points)a.Z120√1 − x2dx =—————————Answerb.Zcsc−1(x) dx =—————————Answer44. (10 points)a. Is the following integral convergent or divergent:Z∞−∞1 − x1 + x4dx.—————————Answerb. ComputeZ21x√x2− 1dx =—————————Answer55. (10 points)a. Use the midpoint rule to estimate the value ofR20cos(x2) dx with the number of intervalsequal to 5.—————————Answerb. Use any approximation method you wish to estimateR10x32dx and make sure that theintervals are fine enough so that the error is less than120.—————————Answer66. (10 points)a. Calculate the following antiderivative:Zx + 1(2x + 1)(3x − 1)2dx =—————————Answerb. Calculate the following antiderivative:Zdx(x + 1)2(x2+ x + 3)=—————————Answer77. (10 points)a. Calculate the arc-lengh of the curve given by the graph y = x2where 0 ≤ x ≤ 2.—————————Answerb. An object is thrown from ground level on a flat landscape into the air with a horizontalvelocity of 2feetsecondand a vertical velocity of 32feetsecond. The acceleration due to the force ofgravity is 32feetsecond2. When the object hits the ground, what is the length of the arc that theobject