Limits
This rule is used to a evaluate limit that is an indeterminate form by simplifying the expression.
What is L'Hopital's rule?
The derivative of a function at a point represents the slope of this line at that point.
What is the tangent line?
This type of integral calculates the area under a curve between two specific x-values.
What is a definite integral?
When approximating integrals, this method uses this formula: ½(a + b)h.
What is a trapezoidal approximation?
These men invented Calculus (2 people).
Who are Newton and Leibniz?
This is the behavior of a function at a point where the left-hand limit does not equal the right-hand limit.
What is a discontinuity?
This rule is applied when differentiating a composition of two functions, such as f(g(x)).
What is the Chain Rule?
Don't forget this!
What is the Constant of integration?
This technique involves approximating the value of a definite integral by partitioning the interval into small subintervals and using rectangles to estimate the area.
What is Riemann Sum?
Eames's beautiful wife always says this.
This concept describes the behavior of a function that becomes unbounded as the input approaches a particular value.
What is a vertical asymptote?
This test is used to determine whether a critical point is a local minimum, local maximum, or neither.
What is the Second Derivative Test?
This theorem connects differentiation and integration.
What is the fundamental theorem of calculus?
This approximation method uses the derivative at a given point to estimate values of a function near that point.
What is a tangent line approximation?
This is the maximum number of derivatives you can take for smooth functions.
What is infinity?
This theorem is used to evaluate limits of a function that is "trapped" between two other functions, whose limits at a particular point are the same, ensuring that the original function also approaches the same value.
What is the Squeeze Theorem?
When a function involves both x and y variables in an equation, this method is used to differentiate both sides of the equation with respect to x.
What is implicit differentiation?
This condition must be true about a function for the Fundamental Theorem of Calculus to apply on a closed interval [a,b].
What is Continuity?
This technique estimates the value of a function at a point using the average of the values of the function at points on either side of the target point.
What is the midpoint approximation?
Eames got a warning for this last year.
What is texting and driving?
This man was the first person to explore limits to calculate areas and volumes.
Who is Archimedes?
Perhaps the first derivatives trade happened around 1800 BC in Mesopotamia, which is now called this. (country)
What is Iraq?
The first documented systematic technique capable of determining integrals is the method of exhaustion created by these two individuals. (Hint: Not Newton and Leibniz)
Who are Eudoxus and Democritus?
This man laid the groundwork for the theory of non-Euclidean geometry, which is crucial for Einstein's theory of general relativity.
Who is Bernhard Riemann?
This is the day on which the first 5 Mu Alpha Theta hours are due (the best day of the year).
What is January 17th, Eames's birthday?