Limits
The value of a limit must be _______.
What is finite?
The derivative represents the _____ of our function.
What is the slope or rate of change?
The integral is the ________________ of our function/graph.
What is the area under the curve?
The function must be continuous and is used to check if a certain value exists on our interval.
What is the Intermediate Value Theorem?
When the sign of both my 1st and 2nd derivative is the same.
What is speeding up?
A limit that has 0 over 0 or infinity over infinity.
What is indeterminant?
The lim as h --> 0 of f(a + h) - f(h) all over h.
OR
The lim as x --> a of f(x) - f(a) all over x - a.
What is the limit definition of a derivative?
List the 4 approximation methods of integrals.
What is, LRAM, RRAM, MRAM, and trapezoidal approximation?
The function must be continuous and is used to prove that there exists a maximum or minumum value.
What is the Extreme Value Theorem?
The difference between the washer and disk method for integration.
What is the "hole" in our shape... or big r and little r.
When the limit from the left side does not match the limit from the right side.
What is undefined?
The four types of derivative rules.
What is the power rule, product rule, quotient rule, and chain rule.
The integral from a to b of f(x) is equal to F(b) - F(a).
What is the Fundamental Theorem of Calculus?
The function must be continuous and differentiable and is used to prove that at some point the slope of our function must be equal to the average rate of change of the interval.
What is the Mean Value Theorem?
The starting point for our radius for disk/washer volume problems.
What is the axis of revolution?
To find the horizontal tangents of a function.
What is check the limits at infinity and negative infinity?
The first derivative of a function can be used to determine... (3 things).
What is when our function is increasing or decreasing, relative extrema, and critical points?
When taking the indefinite integral make sure to add...
What is +C?
What is wrong with this explanation (fix it too):
Since f(x) is continuous on the closed interval, there exists a value between f(2) = 10 and f(8) = -2 on [2, 8] such that f(5) = 2.
What is f(5) = 2? and f(c) = 2.
The two shapes we used for learning the disk method and the washer method.
What is a pear and a bagel?
When the limit exists but the function value does not equal the limit.
What is a removable discontinuity?
The second derivative of a function can be used to determine... (2/3 things).
What is the concavity of our function, inflection points, and (along with the 1st derivative) relative extrema?
The steps to solve for a particular solution of a differential equation.
What is 1. Separate, 2. Integrate, 3. Solve for C, 4. Isolate, and 5. Select ?
What is wrong with this (fix it too):
Since f(x) is continuous on [-2, 11], then there must at least one value c in (-2, 11) such that f'(c) = -5/3.
What is there is no mention of differentiability on (-2, 11)?
When we integrate/cut our shape and we take the area of that shape to integrate (square, triangle, rectangle, semicircle).
What is volume with cross sections?