Definition of a Limit? (fill in the blank)
The (blank) at a point (blank) is the (blank) of the (blank) line to the graph of (blank) at that point. We find this value by taking the (blank) of the (blank) of the (blank) lines through (blank) and (blank) as (blank) approaches (blank).
Choices:
a
(a, f(a))
cos(x)
derivative
f(a)
f(x)
limit(s)
rate of change
secant
sin(x)
slope(s)
tangent
x
(x, f(x))
(x + a, f(x+a))
zero
Last time tried to use _ to signify blanks, but it messed it up
The (blank) at a point (blank) is the (blank) of the (blank) line to the graph of (blank) at that point. We find this value by taking the (blank) of the (blank) of the (blank) lines through (blank) and (blank) as (blank) approaches (blank).
Choices:
a
(a, f(a))
cos(x)
derivative
f(a)
f(x)
limit(s)
rate of change
secant
sin(x)
slope(s)
tangent
x
(x, f(x))
(x + a, f(x+a))
zero
Last time tried to use _ to signify blanks, but it messed it up
2 Answers
The derivative at a point (x, f(x)) is the slope of the tangent line to the graph of f(x) at that point. We find this value by taking the limit of the slope of the secant lines through (x, f(x)) and (x+a, f(x+a)) as a approaches zero .
Steve M's answer is correct. Here is another correct answer:
Explanation:
The derivative at a point (a, f(a)) is the slope of the tangent line to the graph of f(x) at that point. We find this value by taking the limit of the slope of the secant lines through (a, f(a)) and (x, f(x)) as x approaches a .
