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Chapter 1: Q. 21 (page 135)

In the Squeeze Theorem for limits, we require that l(x) ≤ f(x) ≤ u(x) for all x sufficiently close to c, but we do not require this inequality to hold at the point x = c. Why not?

Short Answer

Expert verified

They are determined by the behavior of the function as x approaches c.

Step by step solution

01

Step 1. Given information.

We have to give the reason for In the Squeeze Theorem for limits, we require that l(x) ≤ f(x) ≤ u(x) for all x sufficiently close to c, but we do not require this inequality to hold at the point x = c

02

Step 2. Reason 

Limits as x→care not determined by the function values at point x=c.

In fact, they are determined by the behaviour of the function as x approaches c .

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