Limits
This rule says that
lim_(x->a)f(x)=f(a)
What is the Substitution Rule?
The following is a function of this type and this degree.
3x^2 -12x+4
What is a polynomial of degree 2?
What is a quadratic function?
This is the domain and range of
sqrt(x)
(0, oo), (0, oo)
This is what we say about a graph when it has a hole, jump, or vertical asymptote.
It is discontinuous.
This formula is know as the quadratic formula, and is used for finding the roots/zeroes/solutions of a quadratic function.
(-b+-sqrt(b^2-4ac))/(2a)
This is one of the tricks we learned for solving limits where we cannot originally plug in a number. We multiply by this quantity to get rid of 0's in the denominator or other forms that do not work.
What is the conjugate.
Remember that the conjugate of
sqrta-sqrtb = sqrta+sqrtb
This is the horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.
There is none.
This is the limit of a constant c.
What is c? (The limit of a constant is that same constant. For example
lim_(x->)5=5
This is the name a the graph of a quadratic function.
What is a parabola?
This is the domain of
1/x
(-oo, 0)uu(0,oo)
These are the three conditions presented in class for a function to be continuous at a.
1) f(x) is defined at a.
2) limf(x) exists. (Right and left side agree.)
3) lim_(x->a)f(x)=f(a)
This theorem says that if one function is between 2 other functions with the same limit at a point a, then the limit of the middle function at that point is the same as the limit of the outside functions.
What is the Sandwich Theorem/Squeeze Theorem?
This is the conjugate of
7+sqrt6
What is
7-sqrt6
This is the horizontal asymptote if the degrees of the numerator and denominator are equal.
What is the ratio of the leading coefficients?
This is what the limit is (in general) if the right-hand limit (+) and left-hand limit (-) are not the same.
What is DNE (does not exist)?
This type of function is a quotient of two polynomials. For example,
(x^3+4x^2-12)/(5x+1)
What is a rational function?
This is the domain of the following function.
f(x)=2/(3*x^2)
(-oo,0)uu(0,oo)
The following function has a single point of discontinuity at this number.
f(x)=(x^2-7x+12)/(x-3)
What is 3?
*Note that in class we learned that this function would be continuous ON ITS DOMAIN, because the only point where it is not continuous (x=3) is NOT included in the domain.
As was said in class, this is the whole point of limits.
What is making sense of answers like
0/0
This is the conjugate of
2sqrt8 +5sqrt5
What is
2sqrt8-5sqrt5
This is the horizontal asymptote if the degree of the numerator is less than the degree of the denominator.
What is y=0?
This is
lim_(Q->0) (sinQ)/Q
What is 1?
Note that the variable does not matter, as long as it is the same variable throughout the problem.
These are some of the things that a trigonometric function includes.
What are
sinx, cosx, tanx, cscx, secx, cotx
This is the domain of the following function:
sqrt(x-8)+4
[8, oo)
This is the domain of
g(x)=||x||
What is all real numbers excepts the integers? This can be denoted as:
RR-ZZ
This is the name of the theorem that says that if a function is continuous on [a,b], where a and b are not the same number, then for any output value between f(a) and f(b), there exists a point c between a and b.
What is the Intermediate Value Theorem?
This is the
lim_(x->1)(sqrt(5x^2+95)-10)/(x^2+3x-4)
What is 1/10?
This is where vertical asymptotes CAN be found.
What are zeroes of the denominator?
*Note that not every zero of the denominator is a vertical asymptote. If the zero can be canceled with the numerator, it will not be an asymptote. Ex.
f(x)=(x^2+8x+15)/(x+3)
This is the answer to the following problem:
lim_(x->2)(x^2-5x+6)/(x-2)
What is -3?
Can somebody show their work and graph this function?
These two types of functions are inverses of each other, and we are allowed to use the substitution rule with either of them.
What are logarithmic and exponential functions?
This is an example of a function with the domain:
(-oo,7)uu(7,oo)
Various answers.
This is the graph of a function with a jump discontinuity.
Various answers. Draw one.
This is when the next SI review session will be held.
What is Thursday, September 12 from 5-6:30 in Pearce 126?
This is the
lim_(z->0)(sqrt(64+z)-8)/z
What is 1/16?
These are the asymptotes of
(x^2+x+5)/(2x^2-4)
What are y=1/2 and
x=+-sqrt2