MATH 2412 Lecture Notes - Lecture 9: Intermediate Value Theorem, Dot Product, Conditional Convergence
If a function is 1 to 1 then a horizontal line only cuts the graph in at most 1 place.
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Limits:
If a function is continuous when it has the same limit on either side of a single point.
Squeeze theorem:
When u have the limit of a function in the form of a fraction divide the top and bottom by the highest
power of x in the denominator
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Fibonacci Sequence is defined as:
Convergent and Divergent Sequences:
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Document Summary
If a function is 1 to 1 then a horizontal line only cuts the graph in at most 1 place. If a function is continuous when it has the same limit on either side of a single point. When u have the limit of a function in the form of a fraction divide the top and bottom by the highest power of x in the denominator. If a function is continuous between an interval a and b where a b, then according to the ivt theorem for any number n between f(a) and f(b) there exist a number c such that f(c)=n. This means that if f(a) is above the axis and f(b) is below the axis, then the ivt theorem can guarantee that f has a root (x-intercept) between a and b. To find an x-intercept between an interval a and b for a function f(x), Continue this process until a precise enough approximation can be given.
