Exam 1 with Solution - Survey of Calculus | MATH 160, Exams of Calculus

Download Exam 1 with Solution - Survey of Calculus | MATH 160 and more Exams Calculus in PDF only on Docsity! Name olution Math 160-04 Exam 1B SHOW ALL WORK. No work will receive little or no credit. Put a box around your final answer. 1. (6 pts) Consider a rectangular corral with a partition down the middle, as shown in the Figure below. (a) Assign letters to the outside dimensions of the corral (b) Write an equation expressing the fact that 5000 feet of fencing are needed to construct the corral (including the partition). Bat+abh = Sooo (c) Write an expression for the total area of the corral. Az2ab 2. (15 pts) What is the limit definition of the derivative? ' = }Am fixthy- £1) fip = jem Tees hoo h. Using the limit definition, show that the derivative of f(x) =3x’ + x—2 is f'(x)=6x+1. Use proper notation. fixtey - FO) DOT) “4 Hth) 2 — [3a x3] A h way bxh¢ ah? oxth 22 —3x* ox 42 i = h he YC bx taht | - Seen ah < pion = 6x73ht } fs = liv Aatcte < [tm (bxehe) = dxtorye|oxt | age wpe 3. (15 pts) Find the limits. If the limit doesn’t exist, write “DNE”. (a) lim(@2x-+ vx —1)(5x +x?) = (2244 \ (8.2427) (4 +i) ( Jot 4) x So tg 4t 2 (b) lim *—4 cs anya oJ %, wpe. ma) 44] pa Sule 3B is mt mm the domain g C&2) (Xt 2} Ixy — ToC _— 2h x K-22 Oo td : es Xen = [im ( _ x +l roe Olas l=) and 0p deesn't facto , 4. (12 pts) Find the equation of the tangent line to the function y = 2x’ at the point where x =1 Pp Slope : yl= p.2aX = EX me y'cry = F 1 =y y . YW = 2- r = 2 Vine W-Ye (x) yr2zt & (<1) \ We aX 5. (35 pts) Find the derivative of each function. Use correct notation. @) y=* (b) f(x) = 2x8 +x? 2x 43 le $. xt e|xt FiO) = joxta ox - | (©) fo=3—e () fa) = 2243) t fe) 23-eot gu i f(z) = ft 348 6 2 (-$) (243) a. (243) ~6 td = -{o CM) - | st - ee _ [ie = -Jogty ?