Chapter 2.5, Problem 49E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Which of the following functions .*f* has a removable discontinuity at *a?* If the discontinuity is removable, find a function *g* that agrees with *f* for *x* ≠ *a* and is continuous at *a*.

(a)

(b)

(c)

(a)

To determine

**To check:** Whether the function

Explanation

**Removable discontinuity:**

The function has a removable discontinuity at

**Calculation:**

Consider the function is,

Expand the function by using elementary algebra,

Then,

To check the existence of the limit as *x* approaches 1.

Hence the limit exists at

(b)

To determine

**To check:** Whether the function

(c)

To determine

**To check:** Whether the function

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P-55ESect-2.6 P-56ESect-2.6 P-57ESect-2.6 P-58ESect-2.6 P-59ESect-2.6 P-60ESect-2.6 P-61ESect-2.6 P-62ESect-2.6 P-63ESect-2.6 P-64ESect-2.6 P-65ESect-2.6 P-66ESect-2.6 P-67ESect-2.6 P-68ESect-2.6 P-69ESect-2.6 P-70ESect-2.6 P-71ESect-2.6 P-72ESect-2.6 P-73ESect-2.6 P-74ESect-2.6 P-75ESect-2.6 P-76ESect-2.6 P-77ESect-2.6 P-78ESect-2.6 P-79ESect-2.6 P-80ESect-2.6 P-81ESect-2.7 P-1ESect-2.7 P-2ESect-2.7 P-3ESect-2.7 P-4ESect-2.7 P-5ESect-2.7 P-6ESect-2.7 P-7ESect-2.7 P-8ESect-2.7 P-9ESect-2.7 P-10ESect-2.7 P-11ESect-2.7 P-12ESect-2.7 P-13ESect-2.7 P-14ESect-2.7 P-15ESect-2.7 P-16ESect-2.7 P-17ESect-2.7 P-18ESect-2.7 P-19ESect-2.7 P-20ESect-2.7 P-21ESect-2.7 P-22ESect-2.7 P-23ESect-2.7 P-24ESect-2.7 P-25ESect-2.7 P-26ESect-2.7 P-27ESect-2.7 P-28ESect-2.7 P-29ESect-2.7 P-30ESect-2.7 P-31ESect-2.7 P-32ESect-2.7 P-33ESect-2.7 P-34ESect-2.7 P-35ESect-2.7 P-36ESect-2.7 P-37ESect-2.7 P-38ESect-2.7 P-39ESect-2.7 P-40ESect-2.7 P-41ESect-2.7 P-42ESect-2.7 P-43ESect-2.7 P-44ESect-2.7 P-45ESect-2.7 P-46ESect-2.7 P-47ESect-2.7 P-48ESect-2.7 P-49ESect-2.7 P-50ESect-2.7 P-51ESect-2.7 P-53ESect-2.7 P-54ESect-2.7 P-55ESect-2.7 P-56ESect-2.7 P-57ESect-2.7 P-58ESect-2.7 P-59ESect-2.7 P-60ESect-2.7 P-61ESect-2.8 P-1ESect-2.8 P-2ESect-2.8 P-3ESect-2.8 P-4ESect-2.8 P-5ESect-2.8 P-6ESect-2.8 P-7ESect-2.8 P-8ESect-2.8 P-9ESect-2.8 P-10ESect-2.8 P-11ESect-2.8 P-12ESect-2.8 P-13ESect-2.8 P-14ESect-2.8 P-15ESect-2.8 P-16ESect-2.8 P-17ESect-2.8 P-18ESect-2.8 P-19ESect-2.8 P-20ESect-2.8 P-21ESect-2.8 P-22ESect-2.8 P-23ESect-2.8 P-24ESect-2.8 P-25ESect-2.8 P-26ESect-2.8 P-27ESect-2.8 P-28ESect-2.8 P-29ESect-2.8 P-30ESect-2.8 P-31ESect-2.8 P-32ESect-2.8 P-33ESect-2.8 P-34ESect-2.8 P-35ESect-2.8 P-36ESect-2.8 P-37ESect-2.8 P-38ESect-2.8 P-39ESect-2.8 P-40ESect-2.8 P-41ESect-2.8 P-42ESect-2.8 P-43ESect-2.8 P-44ESect-2.8 P-45ESect-2.8 P-46ESect-2.8 P-47ESect-2.8 P-48ESect-2.8 P-49ESect-2.8 P-50ESect-2.8 P-51ESect-2.8 P-52ESect-2.8 P-53ESect-2.8 P-54ESect-2.8 P-55ESect-2.8 P-56ESect-2.8 P-57ESect-2.8 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P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-1PCh-2 P-2PCh-2 P-3PCh-2 P-4PCh-2 P-5PCh-2 P-6PCh-2 P-7PCh-2 P-8PCh-2 P-9PCh-2 P-10PCh-2 P-11PCh-2 P-12PCh-2 P-13PCh-2 P-14P

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