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Chapter 1: Q. 41 (page 88)

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.

limx→21x2-4

Short Answer

Expert verified

The value of the limit does not exist.

Step by step solution

01

Step 1. Given Information.

The given function islimx→21x2-4.

02

Step 2. Table of values.

A table can be made as,

Here, the value approaches to ∞.-∞from the right and left respectively.

Therefore, the limit of the function does not exist.

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Most popular questions from this chapter

For each limit limx→cf(x)=Lin Exercises 43–54, use graphs and algebra to approximate the largest value of δsuch that if localid="1648023101818" x∈(c-δ,c)∪(c,c+δ)thenf(x)∈(L-ε,L+ε)

localid="1648023199049" role="math" limx→-1x2-2x-3x+1=-4,ε=1

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.

limx→-2(4-2x)=8

Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes.

Sketch a labeled graph of a function that satisfies the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem follows.
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