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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 Iii0 cos .7: — 1 [10] 10. Find the point on the line 3; = 2.1: + 1 closest to the point (2,1).
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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
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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
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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.
 Fall '08
 Wei
 Math, Calculus

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