Terms
This is where the original power rule comes from.
What is the Method of Increments?
The antiderivative of y'(x) = 6x3.
What is y(x) = (3/2)x4 + C?
The equation for the height of an object dropped from a height of 100 feet.
What is h(t) = -16t2 + 100?
What are the limit, derivative, and integral?
The case of overestimating with integrals is called this.
What is "circumscribed"?
The derivative of z(x)= 1/x.
What is z'(x) = -1/x2?
The equation for an object thrown straight up in the air at a speed of 25 ft/s from a height of 50 ft.
What is h(t) = -16t2 +25t + 50?
This ties together the three central concepts of calculus.
What is the Fundamental Theorem of Calculus?
The case of underestimating with integrals is called this.
What is "inscribed"?
The antiderivative of f(x) = 9x7 + 8x3 - 2x
What is F(x) = (9/8)x8 + 2x4 - x2 + C?
The standard acceleration equation.
What is a(t) = -32?
The derivative is associated with this geometrical property.
The formula for the definition of an integral.
What is the integral from a to b of y(x)dx equals the limit as n approaches infinity of Sn?
The derivative of f(x) = 9x7 + 8x3 - 2x
What is f'(x) = 63x6 + 24x2 -2?
This physical property is represented by the area under the acceleration curve.
What is the change in velocity?
The integral is associated with this geometrical property.
What is the area under a curve?
The formula for the definition of a derivative.
What is dy/dx equals the limit as delta x approaches 0 of delta y/delta x?
The antiderivative of z(x) = 1/x.
Trick Question!
We cannot use the reverse power to take the derivative of this function.
This physical property is represented by the area under the velocity curve.
What is the change is distance or change in height of free fall?
There Pythagorean ideas were at the foundation of the Scientific Revolution.
What are the ideas that the universe is ordered according to perfect mathematical law, divine reason is the orderer, and human reason can discern divine mathematical pattern.