Assignment

Juliana Lecompte and Sofia Schuster

Assignment

1.
Lim 2x­2 + x + 3 / 5x3 + x2 + 2x – 4
n to ∞

Lim 2x­2 + x + 3 / 5x3 + x2 + 2x – 4 * 1/x3 /1/x3
n to ∞

Lim 2/x + 1/x2 + 3/x3/ 5 + 1/x + 2/x2 – 4/x3
n to ∞

Lim 0/5 = 0
n to ∞

2.
Finite Sum

10+5+2.5+1.25
R= .5
S∞ = T1/ 1-R S∞ = 10/.5 = 20

Not Finite Sum

1+2+4+8+16
R=2
S∞ = 1(1-2n/1-R) S∞= 1(1- ∞/-1) Turns positive so: S∞ = ∞ = DNE

3.
Simplify and Evaluate

6
∑ 4+ (n-1)4
n=1

6 6 6
∑ 4 + 4 ∑n - ∑1
n=1 n=1 n=1

24+ 4[3(5) – 6]
24+ 4 (15-6)
24+4(9) = 60

5.
Find the value of any trig function

√ 2

1

1


Sin 45 = 1/ √2 * √2/√2= √2/ 2

6.
Convert

150 to radians π

150 * π/ 180 = 2.68

5 radians to Degrees

5* 180/π = 286.5

7.
Find first rev angles

Cos Ө = 4/5
Cos -1= 36.90
360 – 36.9 = 323.10

Cos it’s positive in the 1st and 4th quadrants

8.
Recursive and Explicit definition

5, 9, 13, 17
D= 4
Recursive def = Start in 5 and add 4 to each term it gives you.
T1= 5
Tn = (Tn-1)+4
T5 = (T5-1) +4
T5 = T4 + 4
T5 = 17 + 4
T5= 21

Explicit def
Tn = 5 + (n-1)4
T6 = 5 + (6-1) 4
T6 =5 + 5(4)
T6 = 25

9.
Find the sum of finite and infinite geometric and arithmetic series.

Arithmetic Finite
1+2+3+4+…+20
S20 = 20/2 (1+20)
S20 = 10(21)
S20= 210

Geo infinite
20 + 5+1.25
S∞ = T1/ 1-R
S∞ = 20/.75= 26.7

10.
Tan Ө = -5/4 quadrant # 2

52 + 42 = R2
√41= R
R= 6.5
Cot Ө = 4/5
Cos Ө = -4/6.5
Sin Ө= 5/6.5
Csc Ө = -6.5/5
Sec Ө= 6.5/4

14.
8 + 10 + 12 +14 +…+22
n
∑8 +(n-1)2
n=1

(22-8/2)+1 = n
n= 8

8 8 8
∑8 + 2∑n - ∑1
n=1 n=1 n=1

64+2[4(9)-8]
64+ 56= 120