Mr. Bly's Math 142 Webpage

bly@math.utk.edu

Final Exam
Fri May 1 8-10am HSS 215

Final Exam FAQ
(Updated Apr 30 at 3:52pm)

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HW Help

 Test 1 HW forThu Jan 15 (7) Find general antiderivative. Then find C. (8) Same as 7 (10) Formula derived in class (11) Plotting (x,f(x)) on graph may help. (13) Uses formula from 10 Email Q&A HW forSat Jan 17 (1) Draw the four rectangles? (2) Area of circle is pi*r^2 (3) Graph & use geometry (6-7) Graph in pieces? (9) What about f(x)=x-1 on [0,4]? (10-12) Same as 3 Email Q&A HW forThu Jan 22 (4) Express answer in terms of e (5) Express answer in terms of ln (6) Consider pieces of f(x) separately Email Q&A HW forSun Jan 25 (2) Note here A(x) is Riemann area on [0,x] (3) Use G(1)=0 to find C exactly for G(x) (4) Similar to 3, but with F(2)=0 (6) Note you started with 50 insects at t=0 Email Q&A HW forThu Jan 29 (5) sqrt(u)=u^(1/2) (7) tan(A)=sin(A)/cos(A) (8) cot(A)=cos(A)/sin(A) (9) sin^8(A)=(sin(A))^8 (11) Similar to 9 (12) Similar to 5 HW forSun Feb 1 (5) Can leave answer in terms of sin^-1 Test 2 HW forSun Feb 8 (2) Chain rule on deriv of cos(2x) (3) The x^2 term will require two iterations (4) Same as 3 (5) Manipulate the equations (7) Similar to 2, with sin(2x) (8-10) Two parts related by derivative? Email Q&A HW forThu Feb 12 (7) substitution is done for you...just integrate Email Q&A HW forSun Feb 15 (3) Set x=k*sinh(theta) where k^2 will cancel (4) Similar to 3, but factor to get a leading 1 Email Q&A HW forThu Feb 19 (2) First factor the denominator (4) Note the factor of multiplicity 2 (5) Note x^2+1 has only complex roots Email Q&A HW forSun Feb 22 (3-4) Note f(x) has vertical asymptote (5-7) Needs u-sub to integrate (8) Needs integration by parts, then L'Hopital Test 3 HW forSun Mar 1 (1) No intersection...only one integral on [a,b] (2) Intersection pts where f(x)=g(x) HW forThu Mar 5 (1) Testing endpts will verify what you see (3) Graph carefully, then two regions (5) x^2+y^2=r^2...circle radius r...center (0,0) Email Q&A HW forSun Mar 9 (1) Make a function of y...A(y) is a circle (3) Find intersections...A(x) is an annulus (4) Same as 3...but A(y) is an annulus (5-6) Riemann rects parallel to rotation axis (7) Note x>=0 yields only one encolsed area HW forThu Mar 12 (1-2) A(x) an annulus...one side of constant r (3-4) Cylindrical shells with modified r Test 4 HW forFri Mar 27 (3) Limit Laws (6) L'Hopital's Rule (7-8) Geometric Series (11) e^(-n)=1/e^n (13-14) Numerator bounded HW forSun Mar 29 (2-4) Factor to get k^0 + k^1 + k^2 + ... (6) Careful accounting for all bounces? (7) Same hint as 2-4 (8) (a+b)/c=(a/c)+(b/c) (9) a_n=(S_n)-(S_n-1) Email Q&A HW forFri Apr 3 (1) Compare or limit compare to 1/n^2 (2) Compare to 1/k^n (3) (a/b)^-n = (b/a)^n. Geometric series. (4-7) Limit compare (8) u=ln(n) Email Q&A HW forTue Apr 7 (1) First rule of series? (2) p-test with alternating series (3) |a_n|=(1/1.07)^n. Geometric?(4) Geometric? (5) p-test (6) First rule? (7-9) p-test & limit comparison (10) p-test with alternating series (11) u=ln(n) HW forThu Apr 9 (7-10) Ratio test used to determine rad of conv,then test endpts to determine interval exactly. (11-12) Factor out constant(s) to get 1/(1-k) Email Q&A HW forSun Apr 12 (1-2) Factor out constant(s) to get 1/(1-k) (3) Use Taylor's Formula (4-8) Use known formulas for e^x, cosx, & sinx (8) You might distribute then combine terms (9) Use Taylor's Formula Email Q&A After Test 4 HW forSun Apr 19 (3) What value for f' maximizes the integral? (6) sin(30*)=1/2 (8) Consider at surface. Then, add to depth. Email Q&A HW forThu Apr 23 (2) Break into pieces (5) Region is an area between curves Email Q&A HW forSun Apr 26 (4) Note region is between 0 and pi/2 (5) Set r=r to find intersection points.Then, (Area in big circle)-(Area in small circle).