Q. 21

Question

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?

Step-by-Step Solution

Verified

Answer

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

1Step 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

2Step 2. Reason

Limits as $x \to c$ are 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 .

Q. 20

Q. 22

Other exercises in this chapter

Q. 19

Graph the functions f(x)=x+1 and g(x)=x2−1x−1, and show that they are equal everywhere except at one point. Then show that f(x) and g(x) have differ

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Q. 20

Graph the functions f(x)=2-x and g(x)=4−x2x+2, and show that they are equal everywhere except at one point. Then show

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Q. 22

Use a geometric argument and the Squeeze Theorem for limits to argue that limθ→0− sin⁡θ=0for sufficiently small negative angle

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Q. 23

Use a geometric argument and the Squeeze Theorem for limits to argue that limθ→0− cos⁡θ=1for sufficiently small negative angle

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