CALCULUS
The difference quotient and the average rate of change.. These are topics that are related to
the concept of derivative and calculus.. for function y equals f of x, a secant line is a lie. that
stretches between two points on the graph of the function.. now the slope have the secret
line between the two points A, F of a and b, f of b. a different version represents the average
rate of change of a function. the difference quotient represents the slope of the secant line
for the graph of y equals f of x. it looks like a single entity,, but it still represents a difference
in x values. let 's work out a formula for the difference. this video will introduce the idea of
limits through some graphs and examples. in this video, we use the formula f of B. of B
minus f of A over B minus A To calculate an average rate of change.. we use the related
formula F of X plus H minus F of X over h to calculate a difference quotient..
The limit as X approaches one of f have X is equal to Ted., but when x is exactly one, my
function is going to have a value of zero and not 10.. The limit does n't care about the value
of F at one. but the limit does care about what happens for x values on both sides of a.. In
general, for any function F of X can guarantee that it lies in an arbitrarily small interval around
l. limits from the left or from the right are also called one sided limits. as x approaches
negative two, our y values are getting arbitrarily large. the limit as x. goes to two of g of x
does not exist because the functions do n't approach any finite number. I prefer to say that
these limits do not exist as a finite number, but they do exist as one. Sided. this video gives
some examples of when limits fail to exist. for this function, f of x graph below, let 's look at
the behavior of f of. X in terms of limits as x approaches negative one, one, and two.
negative one and two are the only two values..
the limit as x goes to zero of sine pi over X or sometimes you 'll see sine one over x. if you
graph this on your graphing calculator and zoom in near x equals zero, you 're gon na see
something that looks roughly like this. it just keeps oscillating up and down. as x goes
towards zero, pi over x is getting bigger and bigger. and that 's wild behavior. not a technical
term, just to descriptive term. let 's look at an example that has this wild behavior forcing a
limit not to exist. limits as x goes to a of f of x and G of x exist as finite numbers that is not
as limits that are infinity or negative infinity. the limit of the sum is the sum of the limits. and
the limit of a quotient is the quotient of limits. we'll see. In a moment that these conditions
hold. the Lemon laws allow us to evaluate limits of rational functions just by plugging in the
The difference quotient and the average rate of change.. These are topics that are related to
the concept of derivative and calculus.. for function y equals f of x, a secant line is a lie. that
stretches between two points on the graph of the function.. now the slope have the secret
line between the two points A, F of a and b, f of b. a different version represents the average
rate of change of a function. the difference quotient represents the slope of the secant line
for the graph of y equals f of x. it looks like a single entity,, but it still represents a difference
in x values. let 's work out a formula for the difference. this video will introduce the idea of
limits through some graphs and examples. in this video, we use the formula f of B. of B
minus f of A over B minus A To calculate an average rate of change.. we use the related
formula F of X plus H minus F of X over h to calculate a difference quotient..
The limit as X approaches one of f have X is equal to Ted., but when x is exactly one, my
function is going to have a value of zero and not 10.. The limit does n't care about the value
of F at one. but the limit does care about what happens for x values on both sides of a.. In
general, for any function F of X can guarantee that it lies in an arbitrarily small interval around
l. limits from the left or from the right are also called one sided limits. as x approaches
negative two, our y values are getting arbitrarily large. the limit as x. goes to two of g of x
does not exist because the functions do n't approach any finite number. I prefer to say that
these limits do not exist as a finite number, but they do exist as one. Sided. this video gives
some examples of when limits fail to exist. for this function, f of x graph below, let 's look at
the behavior of f of. X in terms of limits as x approaches negative one, one, and two.
negative one and two are the only two values..
the limit as x goes to zero of sine pi over X or sometimes you 'll see sine one over x. if you
graph this on your graphing calculator and zoom in near x equals zero, you 're gon na see
something that looks roughly like this. it just keeps oscillating up and down. as x goes
towards zero, pi over x is getting bigger and bigger. and that 's wild behavior. not a technical
term, just to descriptive term. let 's look at an example that has this wild behavior forcing a
limit not to exist. limits as x goes to a of f of x and G of x exist as finite numbers that is not
as limits that are infinity or negative infinity. the limit of the sum is the sum of the limits. and
the limit of a quotient is the quotient of limits. we'll see. In a moment that these conditions
hold. the Lemon laws allow us to evaluate limits of rational functions just by plugging in the
