Chapter 2.3, Problem 53E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

(a) If the symbol

(i)

(ii)

(iii)

(b) If *n* is an integer, evaluate

(i)

(ii)

(c) For what values of *a* does

(a)

To determine

**To evaluate:** The limit of the greatest integer function.

Explanation

**Given:**

**Definition used:**

**Greatest integer function:**

The largest integer that is less than or equal to *x* is,

**Direct substitution property:**

If *f* is a polynomial or a rational function and *a* is in the domain of *f*, then

**Theorem 1:**

The limit

**Calculation:**

**Section (i)**

Obtain the limit of the greatest integer function as *x* approaches right-hand side of −2.

Define the greatest integer function as *x* approaches right-hand side of −2.

Thus, the limit of the greatest integer function as *x* approaches right-hand side of −2 is −2.

**Section (ii)**

Obtain the limit of the greatest integer function as *x* approaches −2.

From section (i), the limit of the greatest integer function as *x* approaches right-hand side of −2 is −2.

Obtain the limit of the greatest integer function as *x* approaches left-hand side of −2 is −3.

Define the greatest integer function as *x* approaches left-hand side of −2

(b)

To determine

**To evaluate:** The limit of the greatest integer function.

(c)

To determine

**To find:** The values of *a* does

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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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