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137 Cards in this Set
- Front
- Back
A is 3 more (greater)than B
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A=B+3
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A is less (fewer) than B
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A=B-3
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A is 2/3 more(greater) than B
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A=B+2/3B = B(1+2/3)
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A is 2/3 less(fewer) than B
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A=B-2/3B = B(1-2/3)
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A is percent more (greater) than B
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A=B+50/100B =B(1+50/100)
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A is percent less (fewer) than B
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A=B(1-50/100)
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B 가 A 보다 300% 만큼클경우, B가A의 4배이다
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B=A(1+300/100)=4A
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A is 3 times as many (much) as B = 3 times as many (much) A as B
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A=3B
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A is no more than B
A is less than or equal to B A is at most B |
A>=B
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A is no less than B
A is more than or equal to B A is at least B |
A<=B
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정수 X의개수
a=<x<=b |
b-a+1
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정수 X의개수
a<x<=b |
b-a
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정수 X의개수
a=<x<b |
b-a
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정수 X의개수
a<x<b |
b-a-1
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even + even
even + odd odd + odd |
even
odd even |
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even x even
even x odd odd x odd |
even
even odd |
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연속인 세 정수
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n, n+1, n+3
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연속인 세 짝수
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2n, 2n+2, 2n+4
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연속인 세 홀수
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2n+1, 2n+3, 2n+5
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prime number
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1과 자기자신만을 약수로 갖는수
2는 유일한 짝수 |
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N=A^a * B^b * C^c
약수의개수 (N을 나눌수 있는 수) |
약수의개수는
=(a+1)(b+1)(c+1) |
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4의multiple
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끝의두자리숫자가 4위배수
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25의배수
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끝의두자리숫자가 25의배수
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3의배수
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각자리 숫자의합이 3의배수
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9의배수
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각자리 숫자의합이 9의배수
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2의배수
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일의자리수가 2의배수
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5의배수
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일의자리수가 0또는 5인수
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6의배수
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2의배수& 3의배수
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12의배수
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4의배수 & 3의배수
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15의배수
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5의배수 & 3의배수
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몫과 나머지
N을 8로 나누었을때, 몫이 q이고 나머지가 r 이다 |
N= 8q +r
N/4 =2q +r-4 |
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주기가 2인수
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4, 9
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주기가 4인수
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2,3,7,8
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주기가 1인수
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1,5,6
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0.333 in fraction
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1/3
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1/3 in decimal
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0.333
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0.5 in fraction
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1/2
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1/2 in decimal
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0.5
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0.75 in fraction
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3/4
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3/4 in decimal
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0.75
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0.167 in fraction
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1/6
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1/6 in decimal
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0.167
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sqr root of 2 is
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1.4
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sqr root of 3 is
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1.7
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sqr root of 5 is
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2.2
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work rate
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1. 전체 일의 양을 1로 놓고 1사긴당 하는 일을 개산
2. 1시간에 함께 하는일 X t =1 (1/6+1/3)t=1 |
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catch
B가 A를 따라 잡는 시간 |
B의 거리 =A가 먼저간 걸리 (이전의 거리) + A거리 (이후의 거리)
20t =10X2 + 10t find t for the 따라 잡는 시간 |
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meet
총거리는 300km A와 B가 마주보는 지점에서 9시에 출발 11시에 만났다 A는 B보다 6km 더 빠르다 B의 속도는 |
총거리 =A거리 + B 거리
300 = Va.t + Vb.t 300 = (Vb+6)2 + Vb2 find Vb |
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avg speed =
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total distance/ time
=total distance/갈때 시간 + 얼때시간 =2d/ d/Vavg +d/Vavg =2/1/Vavg+1/Vavg |
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prime number
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number divisible by 1 and itself
2,3,5,7,11,13,17,19,23 and 29 |
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% change
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p 95
= difference/original x 100 |
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parcentage=
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part/whole X 100
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new price if 20% change (inc)
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R=S(1+20/100)
R= new price S= original price |
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X^0 =
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1
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X^-n=
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1/X^n
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X^a x X^b =
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X^a+b
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(X^a)^b =
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X^ab
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X^a / X^b =
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X^a-b
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(XY)^a
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X^a Y^a
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30^50=
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30^25 x 30^25
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6^25 =
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(3x2)^25 = 3^25 x 2^25
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지수의 합차는 낮은지수로 통일
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p103
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2^x+ 2^x =
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4^x
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when derivative of point is zero?
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meaning that the slope is zero
it is possible that point is a local min or a local max |
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[] = squr root
[a] x [b] |
[ab]
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[]= squr root
a[c] + b[c] = |
a+b[c]
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[] squr root
[25] = |
only 5 not -5
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x^2 = 25
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x is either 5 or -5
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[]= squr root
[x] = |
x^1/2
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x^1/3
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{}=cube root
{x} |
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log 10 (X) = a
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10^a =x
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log (x) is same is
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log 10 (x)
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log (10) =
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log (10) =1
same as log 10 (10)=1 10^a =10 a= 1 |
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log (ab)
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log (a) + log (b)
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log (a/b)
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log (a) - log (b)
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log (1/a) =
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-log (a)
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log (a^B)
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b log (a)
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a2 + 2ab + b2
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(a+b)^2
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a2 + 2ab + b2
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(a+b)^2
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a2-2ab+b2
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(a-b)^2
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a2-b2
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(a-b)(a+b)
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(x-1)(x-3)>0
x is? |
0보다 클땐 항상 바깥범위
x>3 x<1 |
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(x-1)(x-3)<0
x is ? |
0 보다 작을땐 사이 범위
1<x<3 |
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부등식의 연산
3<x<10 1<y<2 x+y ? |
4<x+y<12
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부등식의 연산
3<x<10 1<y<2 xy? |
3<xy<20
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부등식의 연산
3<x<10 1<y<2 x-y? |
x-y = x+(-Y)
3<x<10 -2<y<-1 1<x+(-Y)<9 |
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부등식의 연산
3<x<10 1<y<2 x/y ?? |
x/y = x(1/y)
3<x<10 1/2<y<1/1 3/2<x(1/y)<10 |
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probability
동시에 일어날수 없는 두 사건? a 또는 b |
더한다 +
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a 가 b와 함께 일어나는 경우
and |
곱한다 X
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probability that an event occur + probability that the event does not occur =?
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1
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4i
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24
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5i
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120
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6i
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720
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7i
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5040
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varience
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v^2=(x-mena)^2/n
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standard deviation is
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squr root of varience
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csc
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1/sin
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sec
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1/cos
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cot
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1/tan
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i
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squr root (-1)
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i^2
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-1
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i^3
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i^2 x i
-1 x i = -i |
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i^4
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1
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11X11
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121
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12x11
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132
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12x12
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144
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12X9
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108
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12X8
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96
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vector
a+bi |
a= on the x axis
b= is on the y axis |
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vector equation
what is the r for a point that hs 3 dimenional coordinates of (3,6,8) |
r= 3i+6j+8k
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slope =
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rise / run
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if f(x) then
f'(x) = d/dx f'(x) = dy/dx |
first derivitive
sign of slope of graph at any given point is told by the sign of the derivative |
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dy/dx = 0
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slope is 0
fucntion is constant |
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dy/dx > 0
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postive slope
function is inc |
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dy/dx <0
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negative slope
function is dec |
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for f(x)
f''(x) = d^2/dx^2 f(x) =d/dx f'(x) |
second derivitive
tell concave up(local min) or down (local max) |
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f''(x) >0
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concave up (local min)
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f''(x)<0
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concave down (local max)
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f''(x) = 0
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constant slope
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d/dx [f(x)/g(x)] =
quotient rule |
g(x)f'(x)-f(x)g'(x)/g^2(x)
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velocity v(t)
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first derivativ of position (a(t)
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acceleration (how fast speed change)
a(t) |
second derivative of position
first derivative of velocity |
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d/dx sin(x)
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cos(x) 1
1 is der of x |
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d/dx cos (x)
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-sin (x) 1
1 is der of x |
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d/dx tan (x)
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sec^2(x) 1
1 is der of x |
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d/dx csc(x)
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-csc(x)cot(x) 1
1 is der of x |
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d/dx sec (x)
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sec(x)tan(x) 1
1 is der of x |
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d/dx cot(x)
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-csc^2(x) 1
1 is der of x |
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product rule
d/dx[f(x)g(x)]=f(x)g'(x)+f(x)g'(x) |
f(x)g'(x)+f(x)g'(x)
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if f(x)=e^x
then f'(x) |
f'(x) = e^x
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if f(x)=ln(x)
then f'(x) |
f'(x) = 1/x
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[ = intergral
[cos(x)dx |
sin (x) + C
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[ = intergral
[sin(x)dx |
-cos (x) + c
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[ = intergral
[sec^2(x) |
tan (x) +c
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[ = intergral
[csc(x)cot(x)dx |
-csc(x) +c
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[ = intergral
[sec(x)tan(x)dx |
=sec(x)+c
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[ = intergral
[csc^2(x) dx |
-cot(x)+c
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