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USF / Calculus and Pre Calculus / Calculus 2281 / What is the squeeze theorem used for?

What is the squeeze theorem used for?

What is the squeeze theorem used for?

Description

School: University of South Florida
Department: Calculus and Pre Calculus
Course: Calculus I
Professor: Savchuk
Term: Spring 2016
Tags: calculus 1, engineering calculus, and week 2
Cost: 25
Name: Calculus week 2 notes
Description: These notes cover the topics of squeeze theorem, continuity, intermediate value theorem, and more limits.
Uploaded: 02/06/2016
6 Pages 47 Views 1 Unlocks
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Squeeze Theorem - Squeeze function where both functions go to the same place We also discuss several other topics like What are perpendicular lines?

Don't forget about the age old question of What is a legally recognized union between two people in which they unite sexually?

Proof:

Don't forget about the age old question of Was potter stewart liberal or conservative?

If you want to learn more check out What are the three main types of insurable risks?

Don't forget about the age old question of Which struggles have influenced latin american economies and governments?

1.5 Continuity

If you want to learn more check out What to do with former slaves ?

Informal def: f(x) is continuous at x = a if it does not have a “ break” at x = a (both values at a is equal to the lim)

Formal def is

f(x) is continuous everywhere except x = a, x = b, x =c

Def. f(x) is called continuous from left at x = a if

From right at

Def. if f(x) is continuous @ each pt of an interact then we say that f(x) is continuous on I

* Theorem suppose f(x), g(x), are continuous @ x = a; then so are cf (x), f(x) + g(x), f(x) g(x),

And f(x)/g(x) if g (a) ≠ O

*Thus, the following are continuous as long as denominator is ≠ O

  1. Polynom.
  2. Rational f(x)’s
  3. Continuous on the domain
  4. Trig functions: sinx, cosx, +anx (if )

*If we know that f(x) is continuous at a, to find lim, just compute f(a)

Theorem: supposed 1) f(x) is continuous at x = b

                                 2)

Then

Theorem: If 1) g is continuous @ x = a,

                   2) f is continuous @ y = g (a)

Then F g = f ( g(x)) is continuous @ x = a

Example:

Since  is continuous as comp. of continuous f(x)’s

           =  = sin8 = continuous

Intermediate value theorem (IVT)

1.6 Limits involving infinity

Ex:

Def. velt line x = a is called velt asym to f(x) if either of the following are true

Ex. Find V.A of f(x) = 3x/x-2

But… V.A at x=2

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