MATH 1A MOCK MIDTERM 3 PEYAM RYAN TABRIZIAN Name Instructions This is a mock midterm designed to give you an idea of what the actual midterm will look like Make sure you do it the actual exam will be very similar to this one in length and in difficulty Remember that this midterm is 2 hours long Warning The questions on the actual midterm may look completely different from the questions on this mock midterm although the basic structure will be the same so make sure to study the problems from the related rates and optimization handouts as well 1 2 3 4 5 6 7 Bonus 1 Bonus 2 Total 25 10 15 10 10 10 20 5 5 100 Date Friday July 22nd 2011 1 2 PEYAM RYAN TABRIZIAN 1 25 points Sketch a graph of the function f x e should include Domain Intercepts Symmetry Asymptotes no Slant asymptotes though Intervals of increase decrease local max min Concavity and inflection points x2 2 Your work Note This function is used a lot in statistics it is called the normal distribution function MATH 1A MOCK MIDTERM 3 3 This page is left blank in case you need more space to do question 1 4 PEYAM RYAN TABRIZIAN 2 10 points Use linear approximations or differentials to find an approximate value of 3 01 3 MATH 1A MOCK MIDTERM 3 5 3 15 points Two people start moving from the same point One person travels north at a speed of 3 mph and the other person travels east at a speed of 4 mph At what rate is the distance between the two people changing after 2 hours 6 PEYAM RYAN TABRIZIAN 4 10 points Evaluate the following limits a limx 0 x sin x 1 cos x b limx xex c limx 0 xx MATH 1A MOCK MIDTERM 3 7 5 10 points Find the absolute maximum and minimum of f x x3 3x on 0 2 8 PEYAM RYAN TABRIZIAN 6 10 points Suppose f is an odd function and is differentiable everywhere Let b be given Show that there is a number c in b b such that f 0 c f b b Hint Let a b MATH 1A MOCK MIDTERM 3 9 7 20 points Find the point on the line x y 1 that is closest to the point 3 1 10 PEYAM RYAN TABRIZIAN Bonus 1 5 points Use l Hopital s rule to show f x h 2f x f x h f 00 x h 0 h2 lim Note Careful You re differentiating with respect to h here not x MATH 1A MOCK MIDTERM 3 11 Bonus 2 5 points Courtesy Adi Adiredja Omar didn t get the girl Sad and frustrated he decided to run around the track at the gym When he got to the track one girl who was about to start running captured his attention Omar hurried so they could start running together They started at the same time but then she started running faster Omar sped up but then she passed him again Next thing he knew the two of them were racing At some point she noticed the finish line and yelled out I dont go for losers Omar ran as fast as he could and the race ended in a tie After the race she confidently came up to him and said I dont mean to be rude but I only value smart guys If you can prove the next thing I say I ll go on a date with you She then said We started the race at the same time and the race ended in a tie I claim that at some point during the race we were running at the same speed She smiled at Omar and said Are you smart enough Use Calculus to help Omar Hint Let g t and h t be the position functions of the two runners and consider f t g t h t
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