Basic Functions
The domain of the function f(x) = 4 / (x-3).
All x's except for x=3.
The natural log has this irrational number as its base
The number e
These trigonometric functions do not use the hypotenuse to relate an angle to the parts of a triangle.
Tangent and Cotangent
The cost, C (in dollars), of building a house with an area of A square feet is given by the function C = f(A). What is the Leibniz notation and the units for the derivative, f'(A) ?
dC/dA , dollars per square foot
While arithmetic series are based on addition, what are geometric series based on?
Multiplication
If two lines cross at a right angle, their slopes are related by this equation.
m2 = -1/m1
This function is the inverse of the exponential function.
The logarithmic function
The equivalent degree measure of Π/6 radians
30 degrees
If we look at the curve of a function on a small enough scale, we can assume the function is linear, which allows us to estimate ________.
The instantaneous rate of change.
What is the next term in this sequence:
2, 3/4, 4/9, 5/16...
6/25
This graph of this perfectly symmetrical object cannot be the graph of a function.
A circle
If a and b are both positive constants in an exponential function, Q=f(x)=abx, which values of b will cause the function to exponentially decay?
Any number between 0 and 1.
0<b<1
The period of a Sine wave
2Π
If a function's second derivative is positive on a certain interval, what can we say about the original function on that interval?
You are reading a series in sigma notation. You see that i=0 is written under the Sigma. And there is a 7 on top of the Sigma. How many terms are in the series?
8
If P = f(t) gives the population of a city as a function of time, t, in years, what does f-1(P) represent?
The time at which the population equals P.
Considering the properties of logarithms, what is another way of writing log(a) - log(b).
log(a/b)
On a unit circle, which input angle corresponds to a point whose coordinates are (-√2/2 , -√2/2)?
225 degrees
If h=f(a) gives height, h in inches, of a child aged a years, what is the sign of the first derivative dh/da when 0<a<10 ?
Positive
What is the common ratio of this geometric sequence?
4, 10, 25, 62.5, 156.25,...
2.5
What is the x value of the intercept of the two lines: y = 2x +
and
3x + 2y= 1
-1
If the planet Neptune is about 4500 million km from the sun, and the star Proxima Centauri is about four orders of magnitude more distant, what Proxima's distance from the sun?
About 4.5x107 million km.
If the lengths of two sides of a triangle and the angle in between them are known, what Law can you use to determine the length of the third side?
If f is a function with f(3)=0, then can we say for certain that f'(3)=0 ?
No.
This is the sum of all numbers from 1 to 1002
502503