2311_T1B_solutions_F11

# 2311_T1B_solutions_F11 - MAC2311 Test 1 Form B Name 59...

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Unformatted text preview: MAC2311 Test 1 Form B Name: 59 win :3 n S Fall, 2011 Section: (circle yours) MWF 9:00 MWF 10:00 Calculator allowed. Unless otherwise directed, show work to earn partial credit. 1. An open rectangular box with square base x inches on each side must have a volume of 10 cubic feet. Find a function formula for S(x) , the single—variable function that gives surface area as a function of base dimension x. Simpliﬁcation not required. Geometry Facts: Volume of a box is given by the product of its three dimensions, V = LWH . The surface area of a closed rectangular box is the sum of the areas and its six sides, or S=2LW+2LH+2WH. O x X LL 3=X'X+L+'xll(\7 llowwx2.h W Mfr, as.» areas. of area. o'F t 0 bottom estates mi: in a)... K SCﬂax +ti'x' X2. 1» ire 2. The graph of piecewise-defmed function f is shown for x 2 ——5. Assume the first piece is satin—circular and the second linear. _ Complete the formula for f. . . Jaguar?" Engage; . . .. 'f(x)= ' .r “Xwi’lo if X>5 Smear piece ‘HnwaJL (5/5" 4* (mic) _ Yunnmfx'v") .3:- g”, gal-2.; ‘ ' Y’Sewﬂxwg) _ l: WXHD b) Evaluate each limit: lirg for): 5’ ‘ ﬁx)”: . ' 3. Sketch the graph of one possible function f(x) satisfying all of the given conditions. Label holes; with both coordinates and asymptotes with their equations. x 3 ‘ . domainof f is (“00,3)U(3,4)U(4,+oo) ' _ y ° gigaf(x)=ggf(x)=+w *3 'ﬁmﬂxkxlilggﬂxﬁo « Ergf(x)=ﬁngf(x)=1,butf(2)%3 » giggﬂxkl ' 5 o Wherever f is continuous, its graph is concave up 4. Graphs of f and g are shown. Evaluate each limit. Showing work is not required. Graph of f ' Graph of g a)1i§g3f(x) b)1i_133f(x) +00] c) x§r_§1_g(x)® ogggge) NF 1 ' \$371. 7 . 6) 12am 1 ' i) hm 500+];h1 7 \$41" 1934+ 5. Find each limit by any method. Partial credit will be awarded only if the answer is supported by work,but showing is not required. Circle each ﬁnal answer. - J'iZ +1 21) lim x_4 a {M “WE—2 era’s-Au) was» Mr El? “‘1‘ :“m we a 6, lim Xmas Lea m mﬁwxzc: cwxsbw 6 Comm“ f(x)=_”Y3;i_=ME:2_)W xmz“? will“ clamoim at“: . x2H3x—10 (x~5)(x+2) a) Evaluate each limit: lim f(x)= *— oo lin} f(x) : 4‘" \$9 1212f(x)= .D’JE. E/flvegiltis 6'0“? +9 0 H5 B/Pog' #5 all“? 1)) Evaluate each limit: lim f (x): it 3 3- Jl m ll = 4f“ c) Evaluate each limit: lim f(x)= \ IA-u: t) Sketch the graph. Represent asymptotes using dashed lines, and label each asymptote with its ‘ . eqtiatiorr. Represent the hole with a ' small open circle, and label it with both coordinates. Kill t/xl - ‘ ‘h‘ _1—e-n—: Xe, \m,‘ ﬁght-40 ' .5 7. Kane '3 t2.” ‘lvoncj ' “§"ﬁ . Li. 6y set/mega. ﬂeorem 7. If jug-L S f(x) 3 4+6“ asx approaches+oo , then lim f(x) = x+3 r “m L:- H- ' - l ‘ . m m W »X m '2': lim \$415“): [‘W‘ l+°°/x'" Ho “’“Li” and limQtM )2 (“M gin 6’) q we wax-*3 Y2: X»? m ﬂew X“? “m 7‘: Li 8. a) Identify the x—axis interval(s) over which the function f :2 1 2 is continuous. 36 — x Answer: (*0. 00; ﬁg) U fix?) b) Identify the xwvalues where f (x) = 1110+ cos x) is discontinuous. Answer: ' X 3 "T7 +~ th ) V\ may Maggi” m» at a MT) 5») avg mitt 'm’i‘ege—f’ Ow’ xi 2:: «5:: TV) 2:: Eng i: 53a; a v » ext-5, ifng . 9. Find the k-Vaiue that makes f (x) = k Sin x . continuous at x = 0. k = , 1f xﬁo x iim<€x+5 "2:; €G+§ ‘3'" H‘ gag? w I \im‘ptK) /><'~m“ t ﬂﬂi‘gfﬁé mm ktmﬂgﬁglm: k/ x—aw) I iv a ‘W I hm m r. 70591” x m ‘FaPl‘ await table. “0“ r; f 1:; kg g MW \Imuﬁtx) 2 a and 75(0) 2: € Wain, 50f“ 2W“ J 6 mega deﬁnriﬁm 0‘? 10. Consider f(x)m y . Intechnology this is authored as 6/(1+3e’\(1/x)). a “+1 murij . 1+3€ I ' J” F. u ' g; “m . a) Evaluate eachlimit. Nefe’, livgf \$4.“ “0/ ilmm x w) Ctth LM “3;?” \$6.3 . d; (9 >920 (D x+i§® (a ‘ 33} f (1‘) l+3e°° 135} m) H35” ._ use" :53 f“) . a (p _ r W -' g a -,, 3;, www e "*1 2,9,, l + %m H 0 E b) If the graph has any holes, identify them by giving both coordi ates. (0 C) t Q! i c) If the graph has any asymptotes, identify them by their equations. i -; 3g ‘2 L} ...
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2311_T1B_solutions_F11 - MAC2311 Test 1 Form B Name 59...

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