What is the limit as x approaches a number if the function oscillates around the number.
What is undefined
100
The following are two conditions for continuity:
A. f(a) is defined
B. the limit as x approaches a of f(x) exists
What is the third condition?
What is the limit as x approaches a of f(x) equals f(a)
100
What does the second derivative indicate?
What is acceleration
100
evaluate: integral (2 - x )/ sqrt [ 4 - (x^2)] dx
2 arcsin (x/2) + sqrt [4 - (x^2)] + C
200
Evaluate: arctan(1)
What is pi/4
200
Explain the two pronged definition that must be present in order for a limit to exist
What is the limit from the left and from the right must be equal.
200
Name the three ways that a function can fail to be differentiable
What is A. A corner, B. A discontinuity, C. A vertical tangent
200
In terms of velocity, what does the slope of the tangent line reveal?
What is instantaneous velocity
200
Find the area of the region bounded by the graphs of f(x)=sinx and g(x)=cosx, [pi/4, 5pi/4]
2(sqrt [2])
300
solve:
ds/dt = [(sec t ) (tan t)]/ [ (sec t) +5 ]
s = ln | (sec t) +5 | + C
300
True/False: If f(a) is undefined, then the limit as x approaches a will also be undefined.
What is False: Not Necessarily
300
The position function for an object is given s(t)=6(t^2)+240t, where "s" is the measure in feet and "t" is measured in seconds. Find the velocity of the object when t=2 seconds
246ft/sec
300
How do you tell if a particle is slowing down?
What is if the velocity and the acceleration have opposite signs.
300
evaluate integral dx/ [ x sqrt(ln x)]
2 (sqrt ln x ) + C
400
Evaluate
integral 3/ [ sqrt (3 - 2x - (x^2) ] dx
3 arcsin [(x+1)/2] + C
400
Evaluate: lim as x approaches 1 of [1 - sqrt[2(x^2) - 1]/ [x - 1]
-2
400
Find an equation of the tangent line to the graph of f(x)=(x^2) - 2x - 3 at the point (-2, 5) [in slope-intercept form]
y = -6x-7
400
If (x, f(x)) represents a absolute maximum, what is the signe of the second derivative at that point? why?
negative, because it will be concave down
400
Sketch the region whose areas is indicated by the integral from [0,3] sqrt [ 9 - (x^2)]
see pic
500
What is the horizontal asymptote of the following:
r(x) = (3x^2 + 4)/(x^2 - 4x + 10)
What is y = 3
500
Evaluate: lim as x approaches 4+ of [(x^2) - x ] / [(x - 4)^2]
positive infinity
500
Find dy/dx for the equation (x^3) - 2(x^2)y + 3x(y^2) = 38
[3(x^2) - 4xy + 3(y^2)] / [2(x^2) - 6xy ]
500
Let f(x) = x / (1-x) describe the intervals for which f(x) is increasing and decreasing.
f(x) is increasing for all values where x does not equal 1
500
Find the volume of the solid formed by revolving the region bounded by the graphs
y = sqrt (x - 2) , y = 0 , and x = 6, about the y-axis