HOMEWORK MATH 119

HW1  R6  36,42,54,70    R8  48,50,52,54
HW2  1.1 14,54,62  1.2  16,26,44,54
HW3  1.3 24,26,28,52,82,92,96,98,100,112   1.4  16,20,32,40,42,62,68,78,88
HW4  1.5 16,40,46,62,68,70   1.6  22,26,36,40,48,50,52,72,80
***************************************************************
HW5  1.7 8,10,16,22,26,34,44,62,70,90,102   1.8 34,40,70,72,94
HW6  2.1 18,26,44   2.2  20,60,66,76
HW7  2.3 16,32,46a(also do by plugging 2 in),66,78   2.4  20,46,72,78
HW8  2.5 70,74,80,84   2.6   24,42,46,74,78
***************************************************************
HW9  3.1 12,16,20,22,24,30,46,50(also give the domain and range for both the function and its inverse),54   3.2  28,34,40,44
HW10  3.3 26,32,36,38,44,76,78    3.4  82
HW11  3.5 12,24,30,32,42,46,54,56   3.6  6,10,20,24,28,34
HW12  4.1 40,48,68   4.2 16,22,28,32,40,44,50
***************************************************************
HW13  4.3 20,26,36,46,56  4.4  34,36,38,44,64,70
HW14  4.5 40,42,68  4.6  30,32,52,54
HW15  4.7 10,12,18,48,54,62,68,72,80  5.1  78,88,98
HW16  5.2 10,18,20,28,38   5.3  10,42,48
***************************************************************
HW17  5.4 10,12,22,26   5.5  18,24,36,38,42,44
HW18  6.1 14,16,30   6.2  16,24,26
HW19  6.3 12,14   7.1 26,28,34,40
HW20  7.3 16,18,36,44,58,70  Handout on Intro to Limits(1,2,3,4,5,6)


Questions:
1. Give an example to convince someone that a^n a^m= a^(n+m).
2. Tell if the number is rational or irrational and if it is obvious or not...
Square root 7, pi, .713, .7124124124...., 11/47
3. Prove the pythagorean theorem. (fill in blanks)
4. Square root of a squared is a...true of false, explain.
5. Derive the quadratic formula.
6. Why have complex numbers?
7.Give an example to convince someone that the area of a rectangle is lw.
8.Show the area of a triangle is 1/2 bh.
9.Give an example to convince someone that a^n / a^m=a^(n-m).
10.Give an example to convince someone that (a^n)^m=a^(nm).
11.Give an example to convince someone that a^(-n)=1/a^n
12.Give an example to convince someone that a^0=1
13."FOILing" is repeated use of what property?
14.Derive the distance formula for the distance from (x1,y1) to (x2,y2).
15.Derive the equation of a line with pt (x1,y1) and slope m.
16.What is the equation of a line passing though (x1,y1) with no slope?
17.Show that Ax+By+C=0 is a line provided not both A & B are 0.
18.Derive the equation of a circle with center (h,k) and radius r.
**********************************************************************
19.Prove the remainder when P(x) is divided by x-c is the same as P(c).
20.The number of zeroes (allowing for repeats) of a polynomial is equal to the
_______of the polynomial.
21.The theorem that tells us the number of zeroes of a polynomial, allowing for
repeats is the degree of polynomial is what theorem?
22.Show that ax^2+bx+c = a(x+b/2a)^2 + (c - b^2/4a).
23.Why is it so great to know that ax^2+bx+c = a(x+b/2a)^2 + (c - b^2/4a)?
24.Show z1-bar + z2-bar = (z1+z2)-bar
25.Show z1-bar * z2-bar - (z1*z2)-bar
26.We have VA when the bottom is 0 because you can't divide by 0 and if you almost divide by 0 
you get what kind of number.
27.What sort of asymptote will a rational function have if
a)the bigger degree is on the bottom
b)the top is one degree bigger
c)the top is two degrees bigger
***********************************************************
28.If (a,b) is on the graph of f, then what is f(a)?
29.If (a,b) is on the graph of f, then what is a point on the graph of f inverse?
30.If (a,b) is on the graph of f, then what is f inv of b?
31.What kind of asymptote do exponential funcions have?
32.What is the asymptote of y=-17*5^(31x-55) + 77?
33.Prove the formulas on page 397,398
34 Whast is the asymptote of y = 2log(base b)(x-11) + 12?
35.What kind of asymptote do log functions have?
36.Give an example of something that uses logs.
37.Give an example of something that uses exponential functions.
38.Explain how to take sin (number).
39.Explain why the formula sin^2 x + cos^2 x = 1 is true.
****************************************************************
40. How is the domain of sine restricted so it has an inverse.
41. How is the domain of cosine restricted so it has an inverse.
42. How is the domain of tangent restricted so it has an inverse.
43. The output of the sine inv function must be in what range.
44. The output of the cosine inv function must be in what range.
45. The output of the tangent inv function must be in what range.
46. Fill in blanks in proof of cos(a-b) formula
******************************************************
47. Fill in blanks in proof of law of sines.
48. Fill in blanks in the proof of law of cosines.
49. What two formulas make it so easy to multiply complex numbers
in polar form?
50. When solving triangles why should you be careful when using
the inv sin?
51. On the unit circle, if you start at (1,0) and go counterclockwise
a distance of t, what angle in radians will that create?
52. What is cis(theta) short for?
53. Fill in the blanks to show the sum of the angles in a triangle is 180 degrees.