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)




Math Tutoring Center

Ayres G012
MTWR 9am-5pm
F 9am-3pm

Hodges North Commons (220F)
MTWR & Sun 5pm-10pm


HW Help

Test 1
HW for
Thu 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 for
Sat 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 for
Thu 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 for
Sun 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 for
Thu 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 for
Sun Feb 1
(5) Can leave answer in terms of sin^-1
Test 2
HW for
Sun 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 for
Thu Feb 12
(7) substitution is done for you...just integrate
Email Q&A
HW for
Sun 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 for
Thu 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 for
Sun 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 for
Sun Mar 1
(1) No intersection...only one integral on [a,b]
(2) Intersection pts where f(x)=g(x)
HW for
Thu 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 for
Sun 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 for
Thu Mar 12
(1-2) A(x) an annulus...one side of constant r
(3-4) Cylindrical shells with modified r
Test 4
HW for
Fri 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 for
Sun 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 for
Fri 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 for
Tue 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 for
Thu 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 for
Sun 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 for
Sun 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 for
Thu Apr 23
(2) Break into pieces
(5) Region is an area between curves
Email Q&A
HW for
Sun 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).


Daily Review Answers

Test 1
Fri 1/9
1a 2b 3b 4b 5a 6link
Mon 1/12
1b 2a 3(x^3+2)
Tue 1/13
1b 2b 3a 4b 5a 6b
Wed 1/14
1b 2b 3b 4a 5a 6b
Fri 1/16
1a 2a 3b 4a 5a
Tue 1/20
1a 2b 3b 4a 5b
Wed 1/21
1b 2b 3a 4a 5b
Fri 1/23
1a 2a 3a 4b 5b
Mon 1/26
1b 2a 3a 4b 5b
Tue 1/27
1a 2b 3b
Wed 1/28
1b 2a 3b 4a 5b
Test 2
Fri 2/6
1b 2b 3b 4a 5b
Tue 2/10
1a 2b 3a 4b 5a 6a
Wed 2/11
1b 2a 3a 4b 5a
Fri 2/13
1b 2b 3b 4b
Mon 2/16
1b 2a 3b 4a 5b
Wed 2/18
1b 2b 3b 4b
Fri 2/20
1a 2b 3a 4b 5c
Test 3
Fri 2/27
1b 2b 3b 4b 5b
Mon 3/2
1b 2b 3b 4a 5a
Tue 3/3
1b 2b 3b 4b 5b
Wed 3/4
1b 2b 3b 4a 5a
Fri 3/6
1b 2a 3a 4b 5a
Mon 3/9
1a 2b 3b 4a 5a
Tue 3/10
1a 2a 3b 4b 5a
Test 4
Mon 3/23
1a 2b 3b 4a 5b
Tue 3/24
1b 2a 3a 4b 5b
Wed 3/25
1b 2b 3b 4a 5b
Fri 3/27
1a 2b 3b 4b 5b
Tue 3/31
1b 2a 3a 4a 5a
Wed 4/1
1b 2b 3c 4a 5b
Tue 4/7
1a 2b 3a 4a 5b
Wed 4/8
1b 2b 3b 4b 5b
Fri 4/10
1a 2b 3a 4b 5b


Weekly Quizzes

Test 1
(Solutions)
Quiz Fri 1/16
Hints
Solutions
Quiz Fri 1/23
Hints
Solutions
Quiz Wed 1/28
Hints
Solutions
Skills Checklist
Test 2
(Solutions)
Quiz Fri 2/6
Hints
Solutions
Quiz Fri 2/13
Hints
Solutions
Quiz Fri 2/20
Hints
Solutions
Skills Checklist
Test 3
(Solutions)
Quiz Fri 2/27
Hints
Solutions
Quiz Fri 3/6
Hints
Solutions
Quiz Tue 3/10
Hints
Solutions
Skills Checklist
Test 4
(Solutions)
Quiz Fri 3/27
Hints
Solutions
Quiz Thu 4/2
Hints
Solutions
Quiz Fri 4/10
Hints
Solutions
Skills Checklist
Final Exam
(Solutions)
Quiz Wed 4/22
Hints
Solutions
Final Checklist


Khan Academy

Test 1
Fri 1/9
(4.9)
The antiderivative
Power rule for integrals
Integral of sin(x), cos(x) & e^x
Integral of x^-1
Mon 1/12
(4.9)
A more complicated integral expression
Initial value problem with pos/vel/acc
Tue 1/13
(5.1)
Summation notation
Approximating area under curve (4 rectangles)
Approximating area under curve (N rectangles)
Wed 1/14
(5.2)
Intro to Riemann Sum
Fri 1/16
(5.2)
Area under curve from graph
Breaking up an integral inverval
Integral of sum of functions
Tue 1/20
(5.3)
The fundamental theorem
Evaluating a definite integral with FTC
Wed 1/21
(5.4)
Swapping the bounds on an integral
Derivative of an integral
Fri 1/23
(5.5)
Area under a rate function
Water in tub problem
Integral and pos/vel/acc
Mon 1/26
(5.6)
Integration by u-substitution
An example using u-substitution
Another example using u-substitution
Tue 1/27
(5.6)
Integral of tan(x) via u-substitution
Area under curve with u-substitution
Wed 1/28
(5.7)
None
Test 2
Wed 2/4
(7.1)
Integration by parts intro
Fri 2/6
(7.1)
Integration by parts (one iteration)
Integration by parts (two iterations)
Integration by parts (manipulating equations)
Integral of ln(x) (by parts)
Mon 2/9
(7.2)
Odd power of sinx or cosx example
Another odd power of sinx or cosx example
Even power of sinx and cosx example
Tue 2/10
(7.3)
Integral using trig substitution
Another integral using trig substitution
A trig substitution w/ an even power of cosx
Part two of the video above
Wed 2/11
(7.4)
Hyperbolic Trig Functions
Fri 2/13
(7.5)
Integration using partial fractions
Mon 2/16
(7.5)
See Fri 2/13
Wed 2/18
(7.6)
A convergent improper integral
A divergent improper integral
Fri 2/20
(7.6)
See Wed 2/18
Test 3
Fri 2/27
(6.1)
Area between two curves
Mon 3/2
(6.1, 6.2)
Area between three curves
Volume by cross-sections
Another volume by cross-sections
Tue 3/3
(6.2)
Volume of a sphere by cross-sections
Volume by shells - Population density
Wed 3/4
(6.2, 6.3)
Average value of a function
Average value example
Mean value theorem for integrals
Volumes of revolution - Disks
Volumes of revolution - Between 2 disks
Fri 3/6
(6.4)
Continuation of shell video from Tue 3/3
Shells with two functions of x
Shells with two functions of y
Mon 3/9
(6.3, 6.4)
Disks - One function - Non-axis line
Disks - Two function - Non-axis line
Shells - Two functions - Non-axis line
Tue 3/10
(6.5)
None
Test 4
Mon 3/23
(10.1)
Convergence of a sequence
A convergent sequence example
Tue 3/24
(10.1)
Geometric sequences
Wed 3/25
(10.2)
Partial sums
Infinite series are a limit of partial sums
Fri 3/26
(10.2)
Finite geometric series formula
Infinite geometric series formula
Infinite bouncing ball and geometric series
Mon 3/30
(10.3)
Comparison test
Comparison test example
Integral test
Integral test example
Tue 3/31
(10.3)
Limit comparison test
Wed 4/1
(10.4)
Alternating series test
Absolute vs conditional convergence
Mon 4/6
(10.5)
Ratio test
Tue 4/7
(10.5, 10.6)
Power series & radius of convergence
Using ratio test to find radius of convergence
Representing a function as a power series
Wed 4/8
(10.6, 10.7)
Maclauren/Taylor series intro
Thu 4/9
(10.7)
Series for e^x
Series for sinx
Series for cosx
After Test 4
Wed 4/15
(8.1)
Arc length formula
Arc length example
Mon 4/20
(8.2, 8.4)
Idea behind Taylor's theorem
Tue 4/21
(8.3)
Center of mass basics
Wed 4/15
(11.4)
Area between f(theta) and origin
Example with area between f(theta) and origin