Final Exam with Answers Key - Analytic Geometry and Calculus I | MATH 170, Exams of Analytical Geometry and Calculus

Download Final Exam with Answers Key - Analytic Geometry and Calculus I | MATH 170 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Math 170 Name KEY Common Final Exam Section # (circle one): Spring ‘03 or 02—s«B 04 05 NO CALCULATORS OF ANY KIND ALLOWED. Terrio Peterson Trigsted You must show appropriate work to receive credit. 1. (15) Evaluate each of the following limits. ne 5e3 oe ro (Bt DGD = bows (2x+) - 241 {=] be jim 2 ; = @in as SS GeO) XS ey 33 . 2 Ox* Rye . 22-6478 ion Qe SE TS z £43 6-04; ylim St] Ae = > xe Kee les, Re = on Ot? 4 % y TO _ = Sa lon 1 + a S yo 13 Te ne mao (c) lim ethove Seen tyx a xeh oX 2 he w he t ray h re = ; shawn = Vx esx ho h Liew +f) hte n(ixte tk) noo dew tx ! ( a ea oem VRID Ty K los 2. (10) Use the limit definition of the derivative to verify that _f’(x) = 8x—3 when f(x) = Ax? —3x. £'(«)- i. Fox) -£) 2 jk U(x ny Bla — (1x 23x) hora ww h-vs hn _ 4 (x24 2xlrth2)- Sx -Shy ox? Sx = lew , ho hw jw Neer 8x PUht— Sx —SL xt +3 no w haw Bx +¥h*~ Sh = haw Bxrth—-3 = Sx +O-$ ho n hao = Sxe-S 4 3 3. GO) If f(x) = 2x° +5x5 —1, find an equation of the tangent line to the curve at the point where x = | Flee Gx FE Os = Gxt esx fowgente Slaps at xe hs L1G Gts=t yocsor dena be ab x71: £002 235-1 =G et slope ent ug’ \aee - (y~ Qs $Cx-s) 4, (35) Differentiate the following functions. You need not simplify. Zz wsmea rial! = Sx 14 12x ls ) ge = qeiret £2 Sale fie Ro 4 (= Bee) =) ein y* x 42 \ Ke ()y =e In3x ; Brodie t Cole yay *« 2x " " re Og QE eee (d) A(x) = tan® 7x bln) lean ta)® WG = Bear Fx) + Sec*C «TF Witx) 2 1M tantix) 2G | Ore fey NO (F=f (e+ t)*de [WiGas IN tes a F(«)= (xt+)" ~2e ~=«F 2 (xt+ i)" 5. (5) If g(x) is the inverse of f(x) =Inx+3x—1, find g(2). fC): ladiy+ 309-1 2 Zo fF '(x)= +3 t , (2) = 3 eay tl 6. (5) Sketch a graph of a function that satisfies all of the following. so=4 — f@=2 ho asymptote fM=9 f'Q)=0 im fO9=5 fim FO)= ov 13, (35) Integrate. (a) J(e +4 S)ae = f a " () fsin’ 9 cos@ae = furtde = uF tC = | 28 4 C., fet we sn € 3 z daz ws6de ge we xt » f ye [yA des bord (c) [xe* dx let wr % r xe , & > e dv =2x« dx i Ba ody et “+= tem ae ZK wm 2 eee ~ ne - z ~ 7 — a rn Jae fet Uwe KES ax dx &Xx dw = Lol x45 2 LA x x dw 4x dx gu x axe 4% — 2lalule = [2lntxtsl+¢ i Ss (e) [sect xax = Car (®) | “ © tear (£\ ~ 0 Oo 14. (10) A force of 80 N is required to hold a spring stretched 2 meters beyond its natural length. Find the work done in stretching this spring 3 meters beyond its natural length 2 Worle We f Odd we fox dx : 2,8 2° Hooke 's Lav: Fak x = Y4Ox" | = 2Ox*| 2 eo o Ron= KZ =o - © yo 2K = {iso Tf £lx\+ 1Ox 15. (10) Sketch and shade in the region in the first quadrant bounded by the parabolas a 3x? and y = 24~3x*. Find the area of this region. Zz . 4 ° FAS x elves A qarterse chee ! qa — yee Solve vo Ve 2x4= 2H -3x%% age Gxte 24 Zon yte X= te => % 220 Siata Ln 13% quad’ Ona, oly lool ws Ww 2A LY “¥, dx Since Y2 PY, aS (0,2) 4 2 to A > foneaxt 3nd - [24-oxtdy < 24x-2x'| =4S-Ib oO o a 16. (10) The region below is formed by y= 6x — x” and the x-axis. YE Borin FRG (a) Set-up the integral you would use to find the volume of the solid generated by revolving this region about the x-axis, Do not evaluate; just set-up the integral. o [or (bx- x2)" dx © (b) Set-up the integral you would use to find the volume of the solid generated by rev the y-axis. Do not evaluate; just set-up the integral. G Ve f trl ox x? dx 6 olving this region about