Old Exam 1 with Answers - Calculus and Analytic Geometry | MATH 221, Exams of Analytical Geometry and Calculus

Download Old Exam 1 with Answers - Calculus and Analytic Geometry | MATH 221 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! QUESTION 1 (___/20) Use the precise definition of a limit to show that lim, vil-—ic= 2343 ANSWER Gun €70 We Wont FRI € ~E< FRAY <E G-€< Ji <3 € Nite we Wey 4554 Hag E< Tse all of Hese hye pesitie. flenee Fg ears hep te iwetuality Action Gere |) Ute)" (Y-g) +1 <5 < + (YE) diving by “Freer He erection jr (dey ta (ger ETF < . b< Iy-Calls Ie-(-B8$ lye3ls$ -5< K+3< 5 inf Le 3 {ateep so set o> mpi (Hee - (te) ') es iy “th va qo) 1S at feo “3G sxe 39 PER} 3 Page 2 of 6 aa [oG-e} \~ (446) <Sy< [~(4-e}* [+ (FE) e-5x> “1 (4-e]? ({+E)r> |-5x>G-e)* As belo all of Hex ove porte fo the rmegualicr fay te Slum THE VI=5Kx 2Y-€ €> J) -4¥>-€ [jrm 9s € . as YK QUESTION 4 (___./20) Find the derivatives of the following functions (not necessarily starting from the definition): 2 (a) f(z)= cose) {10 points} 2 f3t—4\~° ; ) gt) = ($5) [10 points] ANSWER , — htesxt eae | Ube Wey C+ stp \* Page 5 of 6  QUESTION 5 ¢ 420) Suppose that the distance an aircraft travels along a runway before takeoff is given by D = (i0/9)#? meters, measured from the starting point and ¢ is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reaches 60 meters per second. How long will it take to become airborne, and what distance will it travel in that time? ANSWER The Speed at time © ) Ve) = | 2 = |S") 2 = 24 (bx) 4 Beause. aircrafts tekes off wher ts Speed NU) = Go m/s => Ver = bom/s he. St = be 3 5 te Bb oar me 1 The Distance before, stalee off 5 3 Piap> = ac = Boar = Blo meters, *, So, tha aiiveratt coitl become airbome, when t= 2] secs °, dud Hill travel Slo meters before air borne, Page 6 of 6