Test 1 Key

# Test 1 Key - MATH 1550 —- 5 Test 1A ‘ 9/14/07 Name 1. A...

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Unformatted text preview: MATH 1550 —- 5 Test 1A ‘ 9/14/07 Name 1. A dynamite blast blows a heavy rock Straight up with a launch velocity of 160 ft/sec. It reaches a height of 3 =160! —- 1612 aﬁer t seconds. Complete the table below to ﬁnd the rock’s average {15] velocity over the given time intervals. ILL (2‘)”: __ (4) 2 15¢ Round answers to three decimal places. CW6 V. J E (Q) 0 t w 1 Qt}; Interval — ’il: ' 2L [1.999, 2] [1.99992] _ : Round to two decimal places for the next answers. lim 5mm (No.60 iim S(t)= 9900 1ims(t)m (it: x~+2‘ x-—)2‘L x-—>2 What is the instantaneous velocity at 2 seconds? 9 (Include the unit of measure) 2. Determine the one-sided limits at c = —-2 and c :1 using the graph below. I 131312- f(x) = 3__ lim f(x)= *00 x—> ~2+ an}: we L 6 lim f(x) = 02) x—> 1' lim f(x)m f 21 17+) 1+ List the values of x Where the function is discontinuous. ’ 21 { LIL Which of these discontinuities is removeable? f How would you redeﬁne the function so that it is continuous here? LC if“) 3 3. For what value of a is f (x) ={ [19] M (kg—f) X43” < 3 _ x continuous at every x? Show ALL work. x23 x2 —-1, 21:12:, (Hint: Use one-sided limits.) =9”{58): 9=éa éa Evaluate each limit algebraically. Show ALL work 4. urns/3 2:2 ~4t—8 :42 Xeo M Q 4?} ,— .— 31m) 4&9 ~8 *= W :1 : MCI-Pg) 4 X30 max} = /. ‘XQO [5} . 1C4”; ML 5. lhn—szgsls 23"” C4, 346%.; /¥U3 525*} x—y-Sx x... ....- [10] X 5') (7g 3} l =- -* / I 9 6 IimSin3x = may , a; / [ 3/7 a. 3/ xal) ' 7 x D a *3- r r "’ 5111 x e 3% M76!) 7 _ 7 [10} 2 2 7. Given Ina—s f (x)SI+Z;—,use the Squeeze Theorem to ﬁnd 11113 f (x).ShowALL work; {101 ' 9. [10] 10. [10] m .3 WWW—9:91) ~90?) Sign 270 Use the Intermediate Value Theorem to prove f (x) = 29" ~— cosx has a root in the interval [—5, 4]. Show ALL work ; \$2 W ~ 100g)“ 6 my, ML \mc ‘33 Q5) Rigorously prove lim (4 m 2x) = 2 using the formal deﬁnition of a limit. xwavl i@’&¥3“&\ =5 [iriﬁr(1‘&@a¥)( :5 kztxulr (,6 :37 G1VME>D wméS‘E/g} wake/at €27 arm—#446 that to .3 Mot—93.50) 21%) 36“)! Given f(x) = «/x+4 , [wag-Jake a) use the limit deﬁnition of the derivative to ﬁnd the derivative at x m 0 . Show ALL Work “Qt-ea :QM‘W “he “a, ‘1)?“ng Ho 3 ppm ‘9‘ W +1 st» ‘ ’3“ 43MB Mira: MR 4 meet? _T__ be 001+?) “‘17! If two ﬁﬂm +013 b) Write the equation of the tangent line to f (x) = xix + 4 at x = O. *‘Jk‘Jgﬁcﬂz Q‘Co) [go—“03 1% a at e “(we ...
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## Test 1 Key - MATH 1550 —- 5 Test 1A ‘ 9/14/07 Name 1. A...

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