Definitions
If the left and right hand limits disagree, we say that the limit
DNE or does not exist
lim(x- > oo) (2x^2-7x+4)/(4x^2-5x-2)
1/2
lim (x - > 1) (x^2-2x+3)
2
Find the average rate of change of the following function on the interval [0, 2]
sqrt(4x+1)
What is 1?
lim (x->1)(-(x-4)/(x^2-6x+8)
What is 1?
If the limit approaching either positive or negative infinity equals a certain value, then we can conclude that there is a _______________ at that value
Horizontal asymptote
If the limit as x approaches a certain value is positive or negative infinity then we can conclude that there is a ___________ at that value
vertical asymptote
The limit as x approaches 2 of
(x^2-2x)/(x^2-x-2)
2/3
Find the slope of the following equation at x=-3
y=x^2
What is -6?
lim (x->(3pi)/4) (2cosx)
What is
-sqrt(2)
If the limit at a certain value equals the actual value of the function, we say that the function is ____________ at that value.
continuous
The limit as approaches positive infinity of
(4x^2+7x+1)/(2x-1)
positive infinity
The limit as x approaches 3 of
(x^2-x-6)/(x^2-9
5/6
Write the equation of the line tangent to the curve at the point x=1 of the following equation
y=x^2-3x-1
What is
y=-x-2
lim (x->5)(x^2-5x)/(x-5
What is 5?
If a function is discontinuous at a value but we can create an extended function to fix the discontinuity then the function has a ___________ discontinuity.
removable
The limit as x approaches positive infinity of
(3x^2+2x-4)/(x^3-1)
What is zero
lim (x->9)(x^2-81)/(sqrt(x)-3
108
What is the equation of the line normal to the curve at x=2 of the following function
y=1/(x-1)
What is
y=-x+3
lim (x->-3)(x/(1/(3+x)-1/3))
What is 0?
This theorem tells us that if a function is continuous on a closed interval [a, b] then the function will take on every value between f(a) and f(b).
What is the Intermediate Value Theorem?
The limit as x approaches negative infinity of
(4x^3+2x^2-x+4)/(3x^2+2x-5)
What is negative infinity?
The limit as x approaches -4 of
[1/4+1/x]/(4+x)
-1/16
At what point is the tangent to the following function horizontal?
f(x)=2x^2+6x-3
What is the point
(-3/2, -15/2)
lim (x->3)(x-3)/(sqrt(x+6)-3)
What is 6?