221-borisov-07sp01 - Midterm Exam 1 Wednesday Lev Borisov...

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Unformatted text preview: Midterm Exam 1, Wednesday, Feb 14, 2007 Lev Borisov, Math 221, Lecture Section 1‘ DO NOT OPEN THE EXAM BEFORE THE START ANNOUNCEMENT 2 Please write your name and your TA’s name below. Name: TA: Each problem is worth 20 points, for a total of 100 points. Cal- culators are not allowed on this test. Please read each question carefully, it also helps to check afterwards that you have answered each part of each question. You must show all your work to receive credit. When you turn in your paper after the test, make sure the TA checks your name in their list or writes your name doWn. Good luck! [1] Sketch the graph of the function f = 2sin(7ra:) + 1. What is the period of this function? [2] Calculate the following limits. (a)[10PtS] . hm x3 + sin 30 cc—>+oo (1:2 +1)(2:c +1) (b)[10ptsl , 1 —— cos a: 11m —————————- z-—>O $2 Hint: Multiply numerator and denominator by 1 + 00815. You are not allowed to use L’Hospz'tal’s Rule for this exam. ~[2] (20 pts) Please leave blank! [3] For which values of c is the function 5132, 3:20 ffix)~{ 2+:v, a:<c continuous for all x? You must justify your answer. [3] (20 pts) Please leave blank! [4] Use the definition of derivative as a limit to. find the equation of the tangent line to the curve y = x2 + :1: at the point (—3;6). ‘ Please leave - ank! [5] Let f be a function, which is difierentiable at $0. Consider the function go) = we)? I Use the definition of derivative as a limit to ShOW that 91m) = 2f(wo)f'(xo)~ Remarki This is a particular case of the Chain Rule. However, you are not allowed to use the Chain Rule to solve this problem. Please leave blan ! ...
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221-borisov-07sp01 - Midterm Exam 1 Wednesday Lev Borisov...

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