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Flashcards in Math Deck (23):
1

Hyperbola Equation

Ax2+2Bxy+Cy2+...=0

 

B2-AC>0

2

Cos2θ+sin2θ

 

2Cosθ*sinθ

1

 

2sinθ

3

Adjoint

adj|2   3|

      |-1 0|

|0  -3|

|1   2|

4

Eigenvalues

|1  1|

|2  0|

|1-λ      1|

|2      0-λ|

5

Particular Differential Equation

y+4y=3e^(-t)

replace y to solve the equation

y=Ae^(-t)

 

6

Amplitude

of steady-state

y+4y+4y=8sin2t

replace y with some comon factor

yp=Asin2t+Bcos 2t

 

7

Volume of a parabola

V=∫πx2dy  ,0,a

8

the vector field is conservative is zero

The curl

the curl of a vectore field is zero if it is conservative

9

the cross product AxB

A= (4i+2j)

B= (3i+5j)

 

(4*5)- (2*3)

10

Dot Product

A*B

A=(4i+2j)

B(3i+5j)

A*B= (4*3)+(2*5)

 

11

component of A in the direction B 

A=i-4j and B= 2i-4j-4k

A*iB=(A*B)/|B|

={(i-4j)*(2i-4j-4k)]

---------------------

(22+42+42)1/2

 

(2+16)/6=3

12

the diferential equation

y"+3x2y'+sinx=0

is?

x: nonhomogeneous  

X2: variable coefficient

depends in Y:linear

 

 

if its in terms of Y will be nonlinear

 

13

Taylor series

Cos2x

1-(2x)2/2!+(2x)4/4!-....

14

intercept of the line tangent to the parabola 

x=2y2

point: (2,1)

derivada de x

x=4y

y=1/4x+b

replce the point and find b

 

15

i=

i=e(πi/2)

16

e(πi/4)=

=cosπ/4 + i sinπ/4

17

limx-0, f2/g2

f=sin2x

g=x

2sin2xcos2x)/x

2(2cos22x-2sin22x)/1=4

use differenatial in both sides

 

18

dot product in polar form

(1+2i)(5+3i)

=x+yi

re

r=√(x2+y2)

θ=tan-1 (y/x)

degree in polar

19

∫(0,π), x sin2x dx

u=x    dv=sin2xdx

du=dx  v=-1/2cos2x

uv+vdu

20

base 4 number 101.1 to base 10

 

1*42+0*41+1*40+1*4-1

21

base10 number 21.75

into binary form

1*24+0*23+1*22+0*21+1*20

22

which integral be used to provide the socond moment about the x-axis of the area formed by the straight line, the x-axis and the y-axis?

0γ2 x dy

23

with differentiation you can 

find concavity of curve,the location and number of  inflection points