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Chapter 1: Q. 33 (page 135)

Calculate each of the limits in Exercises 29-70.

limx鈫�24+2xx+2.

Short Answer

Expert verified

The value oflimx鈫�24+2xx+2is,2.

Step by step solution

01

Step 1. Given information

limx鈫�24+2xx+2.

02

Step 2. The limit is calculated as below:

limx鈫�24+2xx+2=limx鈫�2(4+2x)limx鈫�2(x+2)[Quotient rule]

=limx鈫�2(4)+limx鈫�2(2x)limx鈫�2(x)+limx鈫�2(2)[Sum rule]

=4+222+2=84=2

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Most popular questions from this chapter

State what it means for a functionf to be continuous at a point x = c, in terms of the delta鈥揺psilon definition of limit.

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx鈫�3x4.

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)=x2,ifx<24,ifx=22x+1,ifx>2.

Write each of the inequalities in interval notation:

0<|x-2|<0.1

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

limx鈫�2+32x-4=0
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