Lesson 372 of 1524
Limits
Differential calculus arose from trying to solve the problem of determining the slope of a line tangent to a curve at a point.
Practice this chapterDifferential calculus arose from trying to solve the problem of determining the slope of a line tangent to a curve at a point. Integral calculus arose from trying to solve the problem of finding the area of a region between the graph of a function and the x -axis.
The integral is also calculated by finding a limit and, in fact, is related to the derivative of a function The slope of the tangent line indicates the rate of change of the function, also called the derivative .
limit — the process of letting x or t approach a in an expression; the limit of a function f ( x ) as x approaches a is the value that f ( x ) approaches as x approaches a. tangent — A tangent line to the graph of a function at a point ( a , f ( a ) is the line that secant lines through ( a , f ( a ) approach as they are taken through points on the function…. integral — also calculated by finding a limit and, in fact, is related to the derivative of a function. differential calculus — the field of calculus concerned with the study of derivatives and their applications.
Worked example
What does “limit” mean in Limits?
- 1Use the wording this chapter gives for limit.
- 2The book says: the process of letting x or t approach a in an expression; the limit of a function f ( x ) as x approaches a is the value that f ( x ) approaches as x approaches a.
- 3Do not use the meaning of tangent. That term means A tangent line to the graph of a function at a point ( a , f ( a ) is the line that secant lines through ( a , f ( a ) approach as they are taken through points on the function….
Result: the process of letting x or t approach a in an expression; the limit of a function f ( x ) as x approaches a is the value that f ( x ) approaches as x approaches a
Why. That is the meaning this chapter gives for limit.
Do not swap limit and tangent. limit means the process of letting x or t approach a in an expression; the limit of a function f ( x ) as x approaches a is the value that f ( x ) approaches as x approaches a. tangent means A tangent line to the graph of a function at a point ( a , f ( a ) is the line that secant lines through ( a , f ( a ) approach as they are taken through points on the function….
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.