Average ROC
Limits
Squeeze Theorem and IVT
Continuity and Discontinuity
Infinite Limits
100
What is 3?
100
If lim x-->4 g(x) = 7, and lim x-->4 h(x) = 2, this is the value of lim x-->4 g(x) - h(x).
What is 5?
100
Prove that there is a value x = c between .5 and 1 such that f(c) = 0 for the function f(x) = y=6x3-2x
Because f(.5)<0 and f(1)>0, by the intermediate value theorem, there is a value c between .5 and 1 for which f(c) = 0.
100
This is the x value of the removable discontinuity for the function f(x) = (x2 - x - 6) / (x2-9).
What is 3?
100
This is the value of lim x-->∞ ((x2-25)/(x2+2x-15).
What is 1?
200
This is the average ROC of f(x) = -x2 over the interval [0,10].
What is -10?
200
This is the value of lim x-->2 (8 - 3x + 12x^2)
What is 50?
200
Prove that the function f(x) = x3 + x + 7 has a solution.
f(-2)=-3 and f(-1)=5 and 0 is between -3 and 5, therefore by the IVT, this function has a solution.
200
This is the type of discontinuity for the function f(x) = (x2 - x - 2) / (x - 2).
What is removable discontinuity?
200
This is the value of lim x-->3+ 9/(x-3)5 .
What is ∞? (This means there is a vertical asymptote!)
300
This is the average ROC of g(x) = -2x +17 over the interval [-10,-7].
What is -2?
300
This is the value of lim x-->10 x/(3 - sqrt(x-9))?
What is 5?
300
If g(x) ≤ f(x) ≤ h(x) for all x between (3, 5) can squeeze theorem be used with g(x) and h(x) as defined below to find lim(f(x)) x →4 ?
g(x) = -(x-4)2 + 5
h(x) = (x2 - 2x - 8)/(x2 - 7x +12)
No
300
This is the value of x at which the function f is continuous.
What is 1?
300
This is the y-value of the horizontal asymptote in the function f(x) = 2x .
What is 0?