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REY peso eee —~~ MATH 1501 Midterm Examination — FORM B Part 1 Show all of your work and justify your answers to each question using complete sentences when necessary. Answers without work or explanation will not result in full credit. Use your computer to check your answers whenever possible. You must choose 5 out the 6 questions to complete. Write OMIT next to the number of the problem that you do not want graded, otherwise it will be assumed that question #1 is the problem that you do not want graded. Each question is worth 7 % points. GOOD LUCK! 1. Use the Squeeze Theorem to prove that lim x° sin (2) =o? x70 * The tango oF ye Sinx is Bi Pa | jrare fore. we know -| 4 sin (e)s \ mall ying He inequality by we ue get -y® <= y® sin (f) = x" Now teke the batt of each pact of Has inequaltly ae Xo lim ~x" « lin x sin (Z) = xe Xo oe Oz lie x” sin (=) = 0 So by He Yao = 7 nef S yes Oe Squeeze Treoren Iie ye sin (8) ve 2, Use the function f(x) = - eu So to evaluate the following: x-1 whenx>0 i a) jum fC) = 1s Alea Co [1% points each] ») lim f(x)=lim = 2* = O cor) ya 60 li it. x1 = el = I e) lim f@)= Bn i = lim ¥2 27.5 | a lim fa}= $e. 2 e) Is f(x) continuous at x = 0 ? Why or why not? No. Ls L(x) Dees Not Exist x0 therefore. ie F(x) # F(e), 20 
