Limits 1
A function is said to be this if the limit from the left and right of point X equals the value of the function at X
What is continuous?
This phrase is used to describe the limit for a graph whose left bound and right bound limits are not equal
What is undefined?
A function has this characteristic when its derivative exists at each point in its domain
What is differentiability?
This is the technique used for finding the derivative of composite functions
What is the chain rule?
The Daily Double. The limit of the graph from the left side of x approaches 4 and the right limit of x approaches 4. However, the function is not continuous due to a hole in the function at the value of the x, also known as this type of discontinuity
What is a removable discontinuity?
There are four types of discontinuities: jump, oscillating, removable, and this kind, where the limit of the function approaches infinity
What is an infinite/asymptote discontinuity?
This quality where a graph of a function does not have any breaks or holes is one of the two characteristics of a function that must be true in order to establish differentiability
What is continuity?
This is a method used to solve for the derivative of the ratio of two differentiable functions
What is the quotient rule?
This is the overarching term for the limit of a function as h -> 0 of f(x+ h) - f(x) all over h, with h being the change in x and x being a specific value in that function’s domain
What is the derivative?
This specific value is the result of taking the limit as n -> infinity (1 + 1/n)^n, with n being a numeric variable
What is e?
A corner like those in absolute value functions where the 1-sided derivatives differ, a cusp in a graph where the slopes approach infinity from one side and -infinity from the other, an undefined slope, and any discontinuity where the function is not continuous at x=a are all characteristics that would prevent a function from being this
What is differentiable?
This is the result of taking the derivative of y = x in relation to y, with this value being called the implicit derivative
What is 1 = dx/dy?
This is the limit as x approaches 0 for a basic sine function graph, where y=sinx/x
What is 1?
This technique is used to evaluate a limit when it is indeterminate, for example 0/0 or infinity/infinity, and requires that one take the derivative of the numerator and denominator before substituting the x value for the limit
What is L’Hôpital’s Rule?
When a function is differentiable, this characteristic of the function must be defined
What is the second derivative?
This is the derivative of (A)^B, where A is a function and B is a constant
What is B(A)^B-1 * the derivative of A?
When given a value k as part of a piecewise limit equation, one must do this to determine the value of k that makes the function of x continuous
What is set the limits from the right and left of x equal to the value of the function at x?
The daily double. This approach to taking the limit of a function is used when x is approaching positive or negative infinity
What is the End Behavior Model, or Power Model?
The 1st derivative of a continuous function is equal to 2x. Considering these pieces of information, this function can be described as being what
What is differentiable?
The derivative of (u/v) being equal to (v(x)*u’(x)-u(x)*v’(x))/v^2 is the formula for this derivative rule
What is the quotient rule?
This is the reason that Calculus majors never throw any parties
What is because you should never drink and derive?