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Chapter 1: Q. 39 (page 88)

Find the limit of the expression using table

limx->2-(x2+x+1)

Short Answer

Expert verified

The limit of the expression is 7.

Step by step solution

01

Step 1. Given expression

The given expression islimx->2-(x2+x+1)limx鈫�2x2+x+1)

02

Step 2. Calculation using tables

Toseewhathappenstox虏+x+1asx->2-wechooseasequenceofvaluesapproachingx=2fromtheleftandrecordthecorrespondingvaluesinthetableasshownbelow.x1.91.991.9992x虏+x+16.516.95016.995.Hence,limx->2-(x2+x+1)Therefore,thevaluesof+x+1approach7

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�46x-1=23.

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

In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

f(x)=(x-3),ifx<0-(x-3),ifx猢�0.

Calculate each of the limits:

limx鈫�蟺2cotxcosx.
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