Limits
Derivatives
Postion
Velocity
Acceleration
Velocity
Acceleration
Antiderivatives
Kruger Stories
100
As you approach a number, this is really the easiest way to find a limit if you can.
What is substitution?
100
The derivative is x2.
What is the derivative of 1/3x3 + c?
100
The ball is being tossed up with v0 = 10 ft/ sec from h0 =100 feet.
What are the initial velocity and initial height of h(t) = -16t2 + 10t +100?
100
Integral
What is another name for antiderivative?
100
The septic tank in back of the welding shop.
What did Mr. Kruger fall into at the age of 3?
200
Sometimes as you approach a number, Kruger will scream, "To infinity and beyond!", really it's a barrier you can't cross!
What is an asymptote?
200
The derivative is ex.
What is the derivative of ex?
200
Velocity is its derivative.
What is the derivative of the position function?
200
It finds the area under a curve.
What is a definite integral?
200
The answer is 25¢ and 10¢.
What was Mr. Kruger's hourly wage and his brothers' hourly wage as children?
300
Not found in the ER or ICU but a very helpful method in finding a limit if certain conditions apply!
What is L'Hôpital's rule?
300
The derivative is
3/(3x+2)
What is the derivative of ln |3x+2| + c?
300
Velocity is its antiderivative.
What is the antiderivative of accleration?
300
It defines a family of antiderivatives so don't forget your + C.
What is an indefinite integral?
300
The answer is the conjugates.
What does Mr. Kruger call his identical twin brothers?
400
f(c) exists, the limit of f(x) as x approaches c exists, and both just happen to be identical!
How is continuity determined?
400
The derivative is 2sec2 (2x)?
What is the derivative of tan (2x) + c?
400
distance, distance/time, distance/time/time
What are the units for position, velocity, and acceleration?
400
The answer is x2 + c.
What this
int2xdx
400
The answer is cleaning a manure spreader.
What was Mr. Kruger's first job as a 9 year old employee of Kruger Welding?
500
At this point, the limit exists at x = c but f(c) doesn't.
What is a hole?
500
The derivative is 9sin2(3x)cos(3x).
What is the derivative of sin3(3x)?
500
Using the graph to depict my latest walk with Rosie, it happened in the interval, [1, 2].
What interval were Rosie and I at rest?
500
The answer is
(x^2+3)^3/3+c
What is
int 2x(x^2+3)^2 dx
500
"Be smarter than the tool you're using."
What did Mr. Kruger's dad say when the young Kruger hit his finger with a hammer?