A function f(x) is one-to-one on domain D if f(a) does not equal f(b) whenever a does not equal b.
What is one-to-one function?
100
If Y=f(X) is continuous at every point of its interior (a,b), then there is at least one point c in (a,b) at which
f'(c) = f(b) - f(a)
-----------
b - a
What is Mean Value Theorem
100
What is the equation for work?
What is W=Fd
100
Lim e^x
x-> +infinity
What is infinity
100
Solve for t algebraically.
e^kt=1/2
What is (ln2)/k ?
200
The slope of the curve y=f(x) at the point P(a, f(a)) is the number m=lim f(a+h)-f(a)
-------------
h-> h
provided the limit exists
What is slope of a curve at a point?
200
If f(X)=C, where c is a constant, on the interval [a,b], then b b
S f(X)dx = S c dx = c(b - a)
a a
What is The Integral of a Constant
200
How much work is done to stretch a spring 3cm using 6N of force?
What is 18N
200
Solve 1
S e^(x+1)
0
What is e - e^2
200
Solve.
x+3
-----------------
x^3 +6x^2 +9x
What is x^2 +3x
300
Assume f is defined in a neighborhood of c and let c and L be real numbers. The function f has limit L as x approaches c if, given any number a, there is a positive number b such that for all x, 0<|x - c| |f(x) - L|<a
What is a limit?
300
Maximum profit (if any) occurs at a production level at which marginal revenue equals marginal cost
What is Maximum Profit
300
What is this equation
T - T = ( T - T )^ ( e^-kt)
s o s
What is Newton's Law of Cooling
300
Find the derivative of
(X^3)+4X
-------------
X
^
e
What is 4(X^3)+8X (X^3)+4X
-------------- * ------------
(X^2) X
^
e
300
Find the limit as X approaches infinity:
Sin(x)
-----------
x
What is 0?
400
Function Domain Range
---------- --------- ---------
y=ArcTan(x) -infinity
What is inverse trig functions
400
If f is continuous on [a,b], then atr some point c in [a,b],
f(c) = 1 b
----- S f(X) dx
b - a a
What is Mean Value Theorem for Definite Integrals
400
What is the equation for Hooke's Law?
What is F=kx
400
Solve for Y when X= -.14265
Ln(4(Y^2)+8Y - 4) = (X^3) + 14X +2
What is Y= 0.5 , -1.5
400
Find the anti-derivative of y= 3(X^2)+2X+16 using
-------------------
(X^3)+(X^2)+16X
substitution when X=2 and Y=1 without a calculator
What is Y=Ln( (X^3)+(X^2)+16X) + (1 - Ln(56) )
500
An expression of the form a(1)+a(2)+a(3)+ ... +a(n)+ ... The numbers a(1), a(2), ... are the terms of the series; a(n) is the nth term
What is an infinite series?
500
If a and b are any two points in an interval on which f is differentiable, then f' takes on every value between f'(a) and f'(b)
What is Intermediate Value Theorem for Derivatives
500
Use Newton's Method to solve (X^3)+3X+1 = 0
X = X - f(X )
n+1 n n
--------
f'(X )
n
What is -0.3221853546
500
If dy and if Y=3 when X=2, use Euler's method
--- = 2X - Y
dx
with five equal steps to approximate Y when X=1.5. Start at X=2 and the change in X is -0.1
What is the value of X=1.5 is approximately 2.61
500
Find the values of A and B that complete the partial fraction decomposition
2X+16 A + B
------------- = -------- --------
(X^2)+X - 6 X+3 X - 2