Squeeze Theorem - Maple Programming Help

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Squeeze Theorem

Main Concept

Given an inequality of functions of the form:

g(x)≤f(x)≤h(x)

 

In an interval [a,c] which encloses a point, b, the Squeeze Theorem states that if:

 

limxbg(x)=L=limxbhx

 

Then:

limxbfx=L

 

 

Within the interval [a,c], the functions g(x) and h(x) are considered to be the lower and upper bounds of f(x), respectively. Thus, the limit of f(x) at point, b, can be determined graphically by finding a lower and upper bound such that:  the limits of the bounding functions at b are equal.

Determine the limit of the function, f(x), by squeezing it between an upper bound, h(x), and a lower bound, g(x), at the point of interest.

 

 

Function

Limit at

Comments

Question:

 

 

Upper Bound
hx= 

 

 

Lower Bound

gx=

 

 

Choose
a and c

a = 
c=

 

 

 

 

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