Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Calc 1 Concepts: Limits
● A limit is a fundamental concept in Calculus that describes the behavior of a function
as the input approaches a certain value
...
As x approaches 0, f(x) becomes very
large (positive or negative)
...

● We can use limits to determine whether a function is continuous at a certain point
...

● Limits can be evaluated using several techniques
...

● Another technique for evaluating limits is factoring
...
This involves
multiplying the numerator and/or denominator by the conjugate of a radical
expression
...

The following is a diagram of a vertical asymptote
...
A function is said to be continuous on an interval
if it is continuous at every point in the interval
...
The slope of
the tangent line to the curve at that point is equal to the derivative of the function at
that point
...
They are used in a variety of applications, including
the study of derivatives and continuity
...


Function approaching horizontal asymptote
● As we approach a certain value, the function may approach a specific value or may
diverge (i
...
, approach infinity)
...

● If the function diverges as the input approaches a certain value, we say that the limit
of the function does not exist at that value
...
In this case,
we are interested in the behavior of the function as the input becomes very large or
very small
...

● (Include a diagram of a graph of a function with a horizontal asymptote to illustrate
this concept)
● The concept of limits is also important in the study of continuity, which is a
fundamental property of functions
...

● If a function is not continuous at a point, we say that it has a point of discontinuity at
that point
...




---