Limits & Riemann Sums
The phrase we use when there is no b for which limx→c f(x) = b
What is "the limit does not exist"?
This is the derivative of 7
What is zero?
∫5dx from 0 to 4
What is 20?
Method for finding the volume of revolution when there is a hole in the object?
What is the washer method?
A job or career that involves calculus
Who are engineers, scientists, economists, credit card companies, biologists, architects, space flight engineers, statisticians, physicists, operations research analysts, graphics artists, and others?
The limit as x→−3 of x^2-x-12/x+3
What is -7?
If h(x) = 2x^2 + 1, this is the slope of the tangent line at the point P(1, 3).
What is 4?
The exact evaluation of ∫ (sin x+2) dx on the interval [0,pi]?
What is 2pi + 2?
When you integrate, you find this under the graph of a function bounded by a closed interval
What is area?
This is the value that a function approaches as the input approaches a value.
What is a limit?
The limit as x approaches a number if the function oscillates around the number is said to be...
What is undefined?
This is the derivative of y = 5x3 - √2x2 + 6x
What is 15x2 - 2√2x + 6?
These are three applications of integrals
What are Area under a curve, Total distance/displacement, Accumulation over time, Average Function Value , Area Between Two Curves, Volumes of Solids of Revolution?
This formula is used to find the area between two curves.
What is ∫(f(x)-g(x) )dx on the interval [a,b]?
The first ______ can solve for 'velocity' and the second ________ can solve for 'acceleration'.
What is a derivative?
This is the limit of sinx/x as x approaches 0
What is 1?
This is the general formula/definition for derivatives (involving limits)
What is lim f(x+h)−f(x)/h as h approaches 0?
This is the integral of the equation's with derivative 25x^3 - 12x^2 + x.
What is the derivative of 25x^4/4 - 4x^3 + x^2/2?
The integral ∫5x^2+3dx from 0 to 4, rounded to 2 decimal places.
What is 118.67?
One of the people credited with inventing calculus
Who is Isaac Newton? Or, who is Gottfried Wilhelm von Leibniz?
Approximate the area under the curve f (x)=x^2+2, -2≤x≤ 1 with a Riemann sum, using six sub-intervals and right endpoints.
What is 8.375?
This is the derivative of y=√(13x^2-5x+8)
What is (26x-5)/(2√13x^2-5x+8)?
This is ∫((2x+1)^2)dx on the interval [-1,3]
What is 57 1/3?
The volume of the solid rotated about the line y= -2 for the region bounded by y=√ x+2) and y=e^2
19.724
A function fails to be differentiable if it has a....
What is a discontinuity, corner, or a vertical tangent?