New!
Sect. 1.1: 19
Sect. 1.2: 35,39,47,49,
Sect. 1.3: 31, 35,37,43
Sect. 1.4: 15,19,25,29
Sect. 1.5: 13,33,37,49,75,77,79,87
Sect. 2.1: 9,11,13
Sect. 2.2: 19,27,29,31,33
Sect. 2.3: 15,25
Sect. 2.4: 1,15,19,22,31(answer:L2,L3,L4,L6), 33 and 35 (use the limit definition of derivative)
1st Midterm
Sect. 2.5: 9,11,17,19,21,25,31,35,37,40,42,46,47,55,61,71,75,76,79,81,83,85
Sect. 2.6: 3,7,11,13,12,21
Sect. 2.7: The Product Rule:7, 9,11,13,21; The Quotient Rule: 23, 25, 29, 33, 35, 37, 39,41
Sect. 2.8: The Extended Power Rule: page.171: 3,5,9,15,17, 19,21,33,35; The combination of rules:11,13,23,27,29,31,37,39,41,43; The Chain Rule: 57,59,63,65,69,71,83,85,93
Sect. 2.9: 3,5,21,29,31,33,35
Sect. 3.1: 3,7,11,13,17,19,21,23,25,27
Sect. 3.2: 1,7,11,13,15,17,33,37,39,41
Sect. 3.3: 1,3,7,9,13,19, 25,33,39,43. Oblique asymptotes: 27, 45
Sample test 2 (there will be 6-7 problems similar to the ones listed): p.162:#13, use the product rule; p162: #37, #41; p163: #87,#91; p171:#7,#9,#29,#71 (a); p176: #37,#27,#41; p199:#7, use either 1st or 2nd derivative test, also find where the function is increasing and where it is decreasing; p215: #39, also find where the function is concave up and concave down; p.232: for the function in #35 find all asymptotes and x,y -intercepts; p232:#7,#9,#11. It should take about 2 hours to do all of these problems
Sect. 3.4: 3,5,11,17,19,25,33,35, 51,53,61,65,67,73,99,105
Sect. 3.5: 1,3,9,13,15,17,19,21,27,29,35,45,47
Sect. 4.1: 7,9,17,19,21,23,25,27,29,31,49,55,63,65,67,69,71
Sect. 4.2: 3,13,17,19,21,25,27,37,41,43,45,47,49,51,53,55,57,59,61,75,79,81 (some of these problems are very short)
Sect. 4.3: 3,5,7,8,9,25,33,35,39
Sect. 4.4: 1,17,21,23,25 (for carbon the decay rate is k=0.01205),35,41
Sect. 4.5: 9,13,15,17,19,21,23,25,27,33,41,42 (ans:4 ln2 2^{x^4} x^3), use logarithmic differentiation for 43 and 45
Sample test 3: Practice problems for the test (sections 3.4,3.5,4.1,4.2,4.3,4.4,4.5): Sect.3.4: # 5,19,25. Sect.3.5: there will be one problem from 3.5. It can be of any kind listed above in 3.5. For practice do at least these: 9,15,27,35,45,47 (solutions to some of these). Sect.4.1: 9,19,67,69,71. Sect 4.2: 45,47,51,53,55,57,79,81,83. Sect. 4.3: 9,33. Sect.4.4: 3,23,27. Sect. 4.5: 13,23,27,41,43.
Sect. 5.1: 1,3,5,9,11,13,15,17,21,25,27,29,43,47,57,59,61,65,67
Sect. 5.2: 1,5,11,13,15,17,41,43,55,57,59,63,67,69
Sect. 5.3: 1 a),c),13,17,23,25
Sect. 5.4: 1,5,9,11,15,19,21,23,27
Sect. 5.5: 1,5,7,9,11,15,17,19,21,25,31,33,35,37,39,41,49,51,55
Sect. 6.1: 3,7
Sect. 6.2: 1(this one is like the problems from Sect. 4.3,4.4),5,7,11 (Sect.4.3,4.4),15,29
Sect. 6.3: 1,3,5,13,29,39
Sect. 6.6: 1,5,7,9,15,17
Sample test 4: Practice problems for the test (sections 5.1 -5.5, 6.1-6.3, 6.6):
Sect. 5.1: 9,11,15,17,21,25,35!,43,57; Sect. 5.2: 1,11,13,17,57,59,63,67,69; Sect. 5.3: 13,17,25; Sect. 5.4: 1,5,11,19,23; Sect. 5.5: 1,9,11,15,17,19,25,33,35,37,49; Sect. 6.1: 3,7; Sect. 6.3: 1,3,5,13; Sect. 6.6: 5,9,15,17.
Sect. 6.7: 1,3,5,7,9,11,13,15,17,19,21,25,33;
Sect. 7.1: 1,2;
Sect. 7.2: 1,3,5,9,13,19,27.
FINAL EXAM: Study all of the four test and the study material for the tests from this page and Sect. 6.7, 7.1, 7.2 (see problems above). You are expected to be able to evaluate limits (both x approaching finite numbers and +/- infinity cases); analyse functions: find the domain of definition, behavior (continuity, increasing/decreasing behavior, concavity, relative max/min, inflection points); know 1st derivative and 2nd derivative tests; find abs/rel max and minima of fucntions if possible; find the equation of the tangent line at a given point; differentiate, integrate (definite, indefinite, improper integrals), know the relation between integrals and area and volume, average value of a function; solve optimization problems, solve exponential growth/decay problems (such as money accumulation, radioactive decay,...); be familiar with ideas and terminology from appications introduced during the semester such as, for example, "double-life", "half-life", "profit", "revenue"," present value", and other; find partial derivatives of functions of more than one variables, solve differential equations using introduced methods, ..... In other words, the exam covers everything we have studied.