terms Flashcards
(26 cards)
who first developed the idea of limits to measure curved figures and the volume of a sphere in the 3rd Century B.C. by carving figures into small
pieces that can be approximated, then increasing the number of pieces, the limit of the
sum of pieces can give the desired quantity.
Archimedes of Syracuse
the value that a function approaches as that function’s inputs get closer and closer
to some number. It is the most essential concept of calculus. Without it, other core
concepts like continuity, the derivative and the integral would not make sense at all
Limit
an expression involving two functions whose
limit cannot be determined solely from the limits of the individual functions
Indeterminate
In setting the values of x, we are just adding and subtracting 0.1, 0.01, 0.001, 0.0001… and so on, whatever the value of c is.
Limits Using Tabular Method
are two different processes. The value of f(c)
finds the value of the function when x=c, whereas the value of evaluates f(x) when x is near but x is not equal to c.
Functional evaluation and limit evaluation
its defined in that point, its limit exists
and the value of the function is equal with its limit.
Continuous
it does not satisfy any of the three conditions.
Discontinuous
A discontinuity where one or both of the one sided limits go toward infinity
Essential Discontinuity
A discontinuity where the two-sided limits exists but are not equal.
Removable Discontinuity -
A set of real numbers that contains all real numbers lying between any two numbers.
Interval
It is one of the most important applications of differentiation
Tangent line
The word “tangent” comes from the Latin word_____ means _____
“tangere” which means “to touch”
A line that touches the graph of the function at that point but is not parallel to the graph at that point.
Secant line
A number that describes both the direction and steepness of the line; technically it is defined as the change in y over the change in x
Slope
The measure of the rate at which the value of y in a function change with respect to the change in the variable x.
Derivatives
- The procedure for finding the exact derivative directly from a formula of the function without having to use graphical methods.
Differential Calculus
The derivative of any constant is always equal to zero.
Constant Function Rule
is equal to 1. Likewise, the derivative of a function on the first degree is equal to its given numerical coefficient.
Identity Function Rule
Make the exponent as the numerical coefficient and subtract one (1) from the given exponent of the variable x. Simplify the derivatives if needed
Power Rule
The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.
Constant Multiple Rule
The sum rule says the derivative of a sum of functions is the sum of their derivatives. The difference rule says the derivative of a difference of functions is the difference of their derivatives.
Sum And Difference Rules
– It is a formal rule for differentiating problems where one function is multiplied by another. Remember the rule in following way. Each time, differentiate a different function in the product and add the two terms together.
Product Rule
– It is a method of finding the derivative of a function that is the ratio of two differentiable functions.
Quotient Rule
e is a formula for computing the derivative of the
composition of two or more functions. That is, if 𝑓 is a function and 𝑔 is a function, then the chain rule expresses the derivative of the composite function 𝑓 ∘ 𝑔 in terms of the derivatives of 𝑓 and 𝑔.
Chain Rule
