math 1550

math 1550 - MATH 1550: Test 2 October 27 2008 mus— Please...

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Unformatted text preview: MATH 1550: Test 2 October 27 2008 mus— Please return this sheet with your exam paper. Show all your work for full credit. Please read the instructions of each problem carefully: [10] 1. Find the derivative f’(.r) if (a) M) : + (b) f(:r) 2 V13 +1, (c) flat) 2 ln(sin:t:). [10] 2. Find an equation of the tangent line to the graph y = .r 2 ‘2. at the point at [10} 3. Calculate i” at the point (2,1) if d1? $2,213 + 2y 2 3:13. [10] 4. Show that [10] 5. Find the linear approximation [(1‘) = flu) -i- f'(n.)(:t‘ — n) {or fit) : COS:L‘Si11.‘t: and (I, : [10] 6. Find the maximum and minimum values of the function y = 3:3 — 3:2 + 1 on the. segment [0, [10] 7. Find the critical points and apply the Second Derivative Test to determine whether the function 3 2 y = :1: 7 6:1: attains a local maximum, local minimum, or neither at the critical points. [10] 8. Find the critical points and the inflection points of the function y z :52 — 43:4. Determine the intervals where the function is increasing and decreasing. [10] 9. Use the l‘l’lospital Rule to evaluate ,.2 lim Iii-0 cos .7: — 1 [10] 10. Find the point on the line 3; = 2.1: + 1 closest to the point (2,1). YA :fiind ‘fl' ‘ - a t -——~ 5m 2 # a 6. cm ‘X {F@"363n9 7 :7 ——\(Sim52(01)5)0 a it)? “EWCSCX f _ , mix %#45 }L(X)<£Ia)x£“KDLX1D * 0 £00: Cbsxsmx 0:33 \ C‘(x\i'8'\91§+.cwlx\ ‘1 _. Tr £0501i ENE ) ’r 7(C9MEE'SWQWX'E _ Moi/S75 (x55 :5 LOO-1.6. i .) ‘1 6X2 41ch 7?”me 9f I ware + 17.0!“ f If “'— (M4110 H X’ch | xzz WW {UK}. I r MATH 1550: Test 1 September 22 2008 Please return this sheet with your exam paper. Calculators and any notes exept for the trigonometry sheet may not be used on this exam. Show all your work for full credit. Please read the instructions of each problem carefully. [10] 1. Let h(:r) : 21‘2 + 1223 + 3. Complete the square and find the minimum value of Mr). [10] 2. Find the inverse of = and determine its domain and the range. H Evaluate the limit if possible or state that it does not exist and explain why. [10] 3. lim 0 7 T melam—t7. m 1—2 [mm.hm4§;—i m—~3 $73 332 7 '33 i 2 10 5. l' —. i J rinjlr2+3r+2 1 1 10 6. lim —— . l ] I—r1+( 33—1 \/$2—1) tanél —sintl DAD sin38 [10] 8. State the Squeeze Theorem. Use. it to evaluate t22cosfl/t). t#0 [10] 9. State the Corollary from the Intermediate Value Theorem. Use it. to show that the equation e722 = .1: has a solution on the interval (0, 1). [10] 10. Check if the function 1 — cosljgil!1.#0 fl””{ 4,x:0 is continuous at :t = 0. Explain why. If not, what type. of discontinuity it has? YA 3W6 l# _ um) ‘ CU¥6 o§e<5 case it badge 1- B : I’CUSZB (0)8610 (I—Cosiéhmusem‘ waggier 9.»; “‘ i 990 Cm%+\ £1, 2 "*1 7 MATH 1550: Test 3 November 21 2008 NAME: .................................... .. Please return this sheet with your exam paper. Show all your work for full credit. Please read the instructions of each problem carefully. [20] 1. Fundamental Theorem of Calculus: Part I. (a) State Part I of the Fundamental Theorem of Calculus. Evaluate the integrals 2 (b) f(7 — (this, 0 3 (c) _f2 Ireldw, (d) ffisin RIdJL‘. 0 [15] 2. Fundamental Theorem of Calculus: Part II. (3) Find the derivative 1/1: d [sin(t2)dt. a 1 (b) Find the antiderivative of if = I}: and F(1) : O. [15] 3. Substitution Method. (a) Evaluate the integral n/Z f cos3 a: sin $033. 0 (b) Find the indefinite integral fr(z2 — 1)3/2d.7:. (c) Evaluate the integral 2 I If 25033:. [15] 4. Area between two curves. (a) Sketch the region enclosed by the graphs of the functions 1 = 8 — 1:2 and y = 2:13. (1)) Evaluate the area of this region. [20] 5. IVIethod of washers. (a) Sketch the region enclosed by the curves y = .122 and y : ‘21: + 3. 1‘) Evaluate the volume of the solid obtained b ’ rotatin ‘ the region about the 3 E5 0 :ir—ax1s. [15] 6. Method of shells. (a) Sketch the solid obtained by rotating the region under the graph of f(.‘r) : 1/152 over the interval [13] about the axis I : 1. (b) Find the volume of this solid. YA ‘1‘15'LA 9'4'3-5 1,97,!" \7’ LE L 4v (00 be Cbmmucm m Ca.r51,-rm, 4/ Emmy: Hay P703 3 2' ‘P : (1—way :7 [7w 4 Hrlzfm J ’5 ) S’lIfldRXQ CEde 9 :. 3421:; 1‘ - S0 S'mfldx E) £011]: 3) /\J.»\ i 0* - r -: r- LIX%%{ “2%4’: 7 n [—5 mm. .4 1% JA- fflmmq m — éeg H “5317+.- V? {q + 1;) .J "J i 3] ...
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This note was uploaded on 04/22/2010 for the course MATH 1550 taught by Professor Wei during the Fall '08 term at LSU.

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math 1550 - MATH 1550: Test 2 October 27 2008 mus— Please...

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