Exam 2 Questions with Answers - Analytic Geometry and Calculus 1 | MATH 1300, Exams of Analytical Geometry and Calculus

Download Exam 2 Questions with Answers - Analytic Geometry and Calculus 1 | MATH 1300 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Math 1300 Exam 2 Name: page 1 of 11 1. (18) (3 points each) Find the indicated derivatives. You DON’T need to simplify your answers. . (i) #"(e) if f(a) = Go + 2) 7! T.% Lith= 3(4% ta) gd +2] (ii) f(x) (the second derivative) if f(a) = sin 2x f'[x)= Gorn) § be)s coax D(y}= ff Joco re _ a. 7 Teo? dy (iii) a a ¢ Ain (Se) J * Sec? (5x¢) | 4 [Sx] if y = tan(5z7) Math 1300 Exam 2 Name: page 2 of 11 d _(iv) _ if y = arctan(5x7) (note: arctan(5zx7) is the same as tan~*(527)) 2. ‘ wte,(5t!) )= i | ten (5x4) | = Tepy wo ae oo [425% x = gfe. yO! 427% ‘°° | | | . OV bd os | Ve J L) o/b. & | a y 10 Math 1300 Exam 2 Name: page 5 of 11 4, (9) Find the equation of the line tangent to the graph of a? + 4y* = 4xy at the point (2, 1). \ 2 Kt Ye = ta THE GRAPH OF i THIS E@uAtloy IS —Yin tty = a. O” ( THE LIWwE Y=, , (x ~2 4 | =O FoR witich THE TAwGEW? V-29 2) LINE 15 THE UWE ~ xh, ITSELF, AT Aw pou ON THE CWE, IMPLICLT DIFFEREWTIANION WILE MoT CopREectzey LEAD T> THE Slope + AT 1): 4) atte ~ Z. Y¥y ) | DY 4 By MW = ¥ (x Pay, tal) ae rb4 a = fy boy + Yy vy “Uh — 4 dy on ty dy “le [(B9 -Ye)J= ty THS STEP LS (LLEGsC 9h - Uy °9 1 5/V CE 34 Yx =O IW THE DEWOM(N ATOR Novice ThE MuMEMATOR 16 O ALSO, Math 1300 Exam 2 Name: page 6 of 11 5. (6) Let f be a function that has an inverse, denoted by f~'. Suppose that f(3) = 2 and f(4) = 6. Find the equation of the secant line (also called chord) to the graph of f~' through the pair of points whose x—coordinates are x = 2 and x = 6. Math 1300 Exam 2 Name: page 9 of 11 8. (12) (3 points each) Engineers testing an all-new electric vehicle determine that, when revved with maximum force from a standing start, the vehicle’s dis- placement from starting position is given by 3 s=5t! s(t)= if (t in seconds; s in feet). (i) What is the average velocity of the vehicle during the first 10 seconds of motion? / ) 2 4/43 | AVA VEL S (10) -$(o) i. + (107) ~ + (9? 5 00 * OVER FIRST = lo~0 —“-~ ° . «~~ oe () Sece | - (ii) What is the average velocity of the waht during the first 32 feet of motion? How MUct TIME Must ELAPSE Fok THE cAk ‘ : TRAVEL 3) C4 Te 4 2 = ost ¢ 5 S(t}=3 AVG VEL s(y)~5 5(o) 7 (p). nC) s# = 30 — #26 0 Step Wan ely a Ae “Y Sleep =/9 Pt / f (iii) What is the instantaneous velocity of the vehicle after 5 seconds of =] 2 TA [see motion? cy stl- 4 | Lf |= = 2}*>— s!($)=%(5") = RS 7 Permanence per NRT (iv) How many seconds does it take for the vehicle to attain an instantaneous velocity of 150 feet per second? Fok wiat 2 ts! s/(fJ=eiSo 2 Math 1300 Exam 2 Name: page 10 of 11 ¢ - 9. (8) (2 points each) Match the graphs of the functions shown in (i)-—-(iii) with the graphs of their derivatives in (a)-(d). For example, if the derivative of Figure (i) on the left is given by Figure (d) on the right, you would enter a (d) in the space after the word “derivative:” under Figure (i). ke Taw Lives AT XFL S58 te. i)”. 1S OAT Y=th MT y (@) StoPE /Is VERATIVE 5 DEMVATIVE (5 _ AT yr derivative: = (b) (ii) Hoke TAN LWES AT X=0,71 So DERIVATIVE Is ;2€L0 FoR (THESE X's derivative: A (iii) und EF ED at i Nué 5 LQ. TO ConVEK derivative: (iv) DERWaTIVE ALWAYS 20 Since S&oOPE is pcways UP AWAD TO ar THE Pigg Lo | | t ! —2 | ] z - y+ derivative: b Math 1300 Exam 2 Name: _ page 11 of 11 + 10. (12) (3 points each) Find each of the following limits. by ii , . . ‘ otk ' tnd ¥ / (i me rina - Fas 7 fain J aay q.. D+ 3a — 22? L top . 643-4 Libis? — (iii) lim —Taw:~C«<“ - LZ — CO x eeu Awotdeh =, LIMITS AT mwEmity METHOD OF QuoTEvTS OF = —*/, Pou¥Moatt des DEPEWA = ONLY ON THE LEADSNE Coker S FA Mame) Arep BN) DEMA A Atéh iv lim (secx ~tanz (iv) lim, ) Pemursin, — — uc. Tee = San K 2S FN ae ofc Co) "foe J . = | J Sax nt CAN ALS) USE TECHAfaud OF cov TubAreS YER