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Chapter 1: Q. 31 (page 135)

Calculate each of the limits in Exercises 29-70.

limx鈫�-1x2-3xx+2.

Short Answer

Expert verified

The value oflimx鈫�-1x2-3xx+2is,4.

Step by step solution

01

Step 1. Given information

limx鈫�-1x2-3xx+2.

02

Step 2. The limit is calculated as below:

limx鈫�-1x2-3xx+2=limx鈫�-1x2-limx鈫�-13xx+2[Sum rule]

=limx鈫�-1x2-limx鈫�-13xlimx鈫�-1x+2[Quotient rule]

=-12--3-1+2=1--31=1+3=4

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements in Exercises 47鈥�60.

limx鈫�5+x-5=0

Write a delta鈥揺psilon proof that proves that fis continuous on its domain. In each case, you will need to assume that 未 is less than or equal to 1.

f(x)=x鈭�2

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.

Write a delta鈥揺psilon proof that proves that fis continuous on its domain. In each case, you will need to assume that 未 is less than or equal to 1.

f(x)=x2

Calculate each of limits:

limx鈫�11sin-1x.
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