The flashcards below were created by user
lacythecoolest
on FreezingBlue Flashcards.

y(x) = M*x + B. The slope of the line normal to y(x) is
1/M

What means the same as "perpendicular"?
normal

(d/dx)( h(x) / g(x) ) =
(h'*g  h*g') / g^2

(d/dx)( a*h(x) + b*g(x) ) =
a*h'(x) + b*g'(x)

(d/dx)( h(x) + g(x) ) =
exp(x)

e=2.718 and e^1 and exp(1) all mean the same thing
true

h'(x) = g(x) and h(x)=cos(x), g(x)=
sin(x)

h'(x) = g(x) and h(x)=sin(x), g(x)=
cos(x)

h'(x) = g(x) and h(x)=x^n. g(x)=
n*x^(n1)

The dependent variable in y(x) is
y

The independent variable in y(x) is
x

The slope of y at x=x1 is
 (d/dx)y(x)  x=x1
 y'  x=x1
 y'(x1)

The value of y at x=x1 is
y(x1)

y' and y'(x) and (d/dx)y(x) and dy(x)/dx and dy/dx all mean the same thing.
true

All of the following are equivalent. The best way to verbalize _____ is yprime.
y'

All of the following are equivalent. The best way to verbalize _____ is yprime of x.
y'(x)

All of the following are equivalent. The best way to verbalize _____ is derivative with respect to x of y.
(d/dx)y(x)

All of the following are equivalent. The best way to verbalize _____ is derivative of y with respect to x.
dy(x)/dx

All of the following are equivalent. The best way to verbalize _____ is (deey buy deex) or (deey deex).
dy/dx

Given two points on a function, the slope between those two points is
rise/run

Derivative operator is a _______ operator
slope

The derivative of a function is a function
true

The derivative of a function that has a constant value is
another function whose constant value is zero

The derivative of a contant is
not defined

The angle theta is the same as
 all of these
 theta  360 deg
 theta + 360 deg
 theta + 2*pi
 theta  2*pi

If an angle has units of degrees, then the degree unit ____ be written, because radians will be assumed otherwise.
must

Any angle given without units is ALWAYS
radians

The sine function
pops out of nature

Time of 1 second is _____ ms
 all of these
 1000
 1,000,000E3
 1E3

me of 123456 us is _____ seconds
0.123456

Time of 123 ms is _____ seconds
0.123

sin(x) = cos(x _____)
pi/2

cos(x) = sin(x _____)
+pi/2

y=A*sin(w*t + theta) + B, B is _____ shift, measured with same unit as ______.
vertical, A

y=A*sin(w*t + theta), theta is _____, measured in ______.
phase shift (or angle), degrees or radians

. y=A*sin(2*pi*f*t), f is
1/T

y=A*sin( t * 2 * pi / T ), T is ______ measured in ______.
periods/seconds

y=A*sin(2*pi*f*t), f is frequency
cycles/second or Hertz

y=A*sin(w*t), w is
2*pi*f

y=A*sin(w*t), t is _____ and w is _____.
time in seconds, frequency in radians/second

y=A*sin(x), A is
amplitude

_____ is unitless because it is defined as arc length / radius
radian

The unit of sin(x) is
none

pi radians is ____ degrees
180

y=sin(x), x can be _____, but without units is always _____.
radians or degrees, radians

Engineering technology students know that Euler's identity (e^(i*pi)+1=0) is easy to understand, because e^(i*pi) is a complex number in polar form and is equal to 1.
true

Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true

Euler's identity (e^(i*pi)+1=0) contains all the special numbers: 0, 1, e, i, and pi, and has been called the most profound equation in all of mathematics.
true

AC voltage of 5*exp(0.927i) has an phase of
0.927 radians

AC voltage of 5*exp(i53.13 deg) has an amplitude of
5 volts

sin(z), cos(z), tan(z), ln(z), log(z) are defined when z is a complex number
true

exp(i*z) is the same as
cos(z)+i*sin(z), which is know as Euler's formula

Complex numbers can be
 all of these
 multiplied and divided
 added and subtracted
 raised to powers
 placed in matrices

The sum of 3 and i4 has an angle of
 both of these
 0.927 radians
 53.13 degrees

The sum of 3 and 4i is
 both of these
 exp(0.927i)*5
 5*exp(0.927i)

exp(i*pi/2)*3=e^(i*pi/2)*3 is a complex number in polar form and is also

exp(i*pi)*2=e^(i*pi)*2 is a complex number in polar form and is also

exp(i*pi)*1=e^(i*pi)*1 is a complex number in polar form and is the same as

exp(1)=e^(1) is known as Euler's number and is
2.71828

The angle (radians) of the sum of 3 and i4 is

The magnitude of the sum of 3 and i4 is
 7
 5
 3+i4
 sqrt(3^2+(4i)^2)


The angle of 3+i4 is
53.13 deg




The number (3+i4) is an example of a _______ number in rectangular form.
complex

Complex numbers
are frequently used in electrical engineering

A complex number is
like a 2D vector


