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21 Cards in this Set

  • Front
  • Back
Consider the relationship involving g(x).
4x ≤ g(x) ≤ 2x4 - 2x2 + 4 for all x
Evaluate the following limit.
lim as x>1 of g(x)
4 (squeeze theorem)
Find the limit, if it exists.
lim as x>9 of (5x+|x-9|)
Find the limit, if it exists.
lim as x>-9 of [(10x+90)/(|x+9|)]
Evaluate the limit, if it exists.
lim as x>0+ of [(1/x)-(1/|x|)]
What does the symbol [[x]] represent?
The greatest integer function. It rounds down to the lower integer
Power function
f(x)=x^a where a is a constant
Does not include polynomials
Is an algebraic function
Ex. x^(1/5)
Root function
Is a power function where a=(1/n)
Is an algebraic function
Ex. x^(1/2)
Polynomial function
where n in non-negative,
a_n are constants,
all values of x are defined,
whole # exponents.
Is a rational function over 1
Is an algebraic function
Rational function
Ratio of 2 polynomials.
Is an algebraic function.
Algebraic function
If it can be constructed using + - * / or taking roots with rational exponents.
Trigonometric functions
Contain sin cos tan sec etc.
Not algebraic functions
Exponential functions
Form f(x)=a^x where
a is a positive constant
Not algebraic function
Ex. e^x
Logarithmic functions
Inverse of exponential functions
Contain logarithms (logs)
Formulae for constructing a function
There's another...
The manager of a furniture factory finds that it costs $2200 to manufacture 50 chairs in one day and $4800 to produce 250 chairs in one day. Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.
slope is 13 which represents the cost of producing each additional chair
y-int is 1550 which represents the cost of operating the factory daily
Define the infinite limit.
lim as x>2 of [(3-x)/(x-2)^2]
Define the infinite limit.
lim as x>3- of [(e^x)/(x-3)^3]
Define the infinite limit.
lim as x>2pi+ of [x*cot(x)]
What happens as v>c-?
There will also be questions about defined (not infinite) limits.
Use simple algebra and some fancy tricks to solve them.
Consider the rational function f(x) = p(x) / q(x)
How can one find the vertical asymptotes?
An asymptote is a line that the curve approaches but does not cross. The equations of the vertical asymptotes can be found by finding the roots of q(x). Completely ignore the numerator when looking for vertical asymptotes, only the denominator matters.

If you can write it in factored form, then you can tell whether the graph will be asymptotic in the same direction or in different directions by whether the multiplicity is even or odd.

Asymptotic in the same direction means that the curve will go up or down on both the left and right sides of the vertical asymptote. Asymptotic in different directions means that the one side of the curve will go down and the other side of the curve will go up at the vertical asymptote.