Derivatives
The derivative is f'(x)=3x^2.
What is f(x)=x^3
You always add this at the end of antiderivatives.
What is "+C"
This is what happen when the left and right limits don't equal.
What is this limit does not exist
One of the two people responsible for inventing Calculus.
Who is Isaac Newton or
Gottfried Leibniz
This is the line that touches a graph at a point and continues in the direction the graph was going at that point.
What is a tangent line?
This is the power rule for finding derivatives.
What is y'=n*xn-1
This is what you find when calculating a definite integral.
What is the area under a graph.
This is the limit as x approaches 3 of 2(x-4)^2
What is 2
The century that calculus was invented.
What is the 17th century
This is the result of the following: ∫(7x+9)dx
What is (7/2)x2+9x+c
The formula you need to use when finding the derivative of two functions multiplied.
What is the product rule...y'=uv'+u'v
This is another name for the antiderivative.
What is the indefinite integral?
If y= (x2-4)/(x-2), this is what occurs when x=2
What is a hole?
These are the two main concepts that were included in the Calculus created by Newton and Leibnitz.
What are derivatives and integrals?
This is what d2y/dx2 means.
What is the second derivative.
This is the rule used for differentiating composite functions.
What is the chain rule?
This is what we get when we integrate 1/(2x-1)dx
What is (1/2)*ln[2x-1]+c
This is the limit of 1/x as x approaches negative infinity.
What is zero?
This is where Leibniz was from.
What is Germany?
This is the area enclosed by y=x2 and the y-axis between [0,3] is revolved around the y-axis
What is (9/2)*pi
A function is not differentiable where it has this.
What is a cusp, discontinuity, or a vertical tangent line.
The derivative of this equation is sec2(x)
What is tan(x)+c
The limit as this expression approaches 2 is infinity.
Answers will vary, but one example is
1/(x-2)2
This was the first nationality of the people on record to use concepts found in calculus before it was actually called Calculus.
What are the Greeks?
These are two different types of discontinuity.
What are point, step, or infinite discontinuity.