Limits at a point
Limits and Infinity
Continuity
Rates of Change
Miscellaneous
100
The symbol that indicates the limit of f(x) as x approaches it approaches from the left and right.
What is - and +?
100
These types of functions limits at infinity are defined by their end behavior.
What is polynomial functions?
100
Any function f(x) whose graph can be sketched without lifting a pencil is an example of a ____________ function.
What is continuous?
100
This type of rate represents the slope of a curve at a specific x value.
What is instantaneous rate?
100
The algebraic technique used here to evaluate the limit.
lim_(x->1)((x-1)/((x-1)^2))
lim_(x-1)((x-1)/((x-1)(x+1)))
lim_(x->1)(1/(x+1))=2
What is factoring?
200
When evaluating a limit, this method is always attempted first.
What is direct substitution?
200
These types of functions limits at infinity are typically defined by their horizontal or slant asymptotes.
What is rational functions?
200
This type of discontinuity would make Mario leap for sure.
What is jump discontinuity?
200
Taking the limit as h goes to 0 of this quotient gives us the expression for the instantaneous rate of the curve at any point x.
What is the difference quotient?
200
The algebraic technique used here to evaluate the limit.
lim_(x->9)((x-9)/(root2(x)-3))
lim_(x->9)((x-9)/(root2(x)-3)*((root(2)x+3)/(root(2)x+3))
lim_(x->9)([(x-9)(root(2)x+3))/(-x+9))
lim_(x->9)(-(root(2)x+3))=-6
What is multiply by the conjugate pair?
300
The limit of f(x) at x exists when these two limits are equal.
What is left and right limits?
300
The limit of the following is ____.
lim_(x->oo)((4x^5-2x-4)/(2x^2+5x-3))
What is infinity?
300
This type of discontinuity would give Mario a chance at a power up or coins.
What is a removable discontinuity?
300
A line that hits the function twice and represents the average rate of change.
What is a secant line?
300
The algebraic technique used to find the limit.
lim_(x->-2)((1/x+1/2)/x+2)
lim_(x->-2)(2/(2x)-x/(2x))/(x+2)
lim_(x->-2)((2+x)/(2x))/(x+2)
lim_(x->-2)((2+x)/(2x))(x+2)
lim_(x->-2)(1/(2x))=-1/4
What is common denominator?
400
lim_(x->4)(1/(x-3))
What is 1?
400
The limit of the function at infinity is _____.
lim_(x->oo)((-5x^5-2x^3+x^2-x+100)/(2x^3-4x^2+x-101))
What is negative infinity?
400
This type of discontinuity, if Mario failed to cross it successfully, would cause him to fall to his demise.
What is an infinite discontinuity?
400
A line that only intersects the graph of f(x) once and represents the instantaneous rate.
What is tangent line?
400
When algebraic techniques are insufficient, we can find the left and right sided limits using _________ or ______.
What is graphs or tables?
500
lim_(x->3)(1/(x-3))
What is DNE?
500
The limit is _______.
lim_(x->oo)(cos(1/x))
What is 1?
500
Give an example of a function that is a continuous function and it's domain is NOT all real numbers.
Something like 1/x.
500
In order to take the limit of the difference quotient, we must use algebraic techniques to cancel out _____.
What is h?
500
Identify a pair of functions for g(x) and h(x) that we could possibly use to find the limit of f(x) using the Sandwich Theorem.
g(x)<=f(x)<=h(x)
What is___?
x^2
|x|
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