   Chapter 10.3, Problem 89E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Processor Speeds The processor speeds, in megahertz (MHz), of Intel processors during the period 1996–2010 can be approximated by the following function of time t in years since the start of 1990: v ( t ) = { 440 t − 2 , 200      if 6 ≤ t < 15 3,800                 if 15 ≤ t ≤ 20. a. Compute lim t → 15 − v ( t ) and lim t → 15 + v ( t ) , and interpret each answer. [HINT: See Example 3.]b. Is the function v continuous at t = 15 ? According to the model, was there any abrupt change in processor speeds during the period 1996–2010?

(a)

To determine

To calculate: The limits limt15v(t) and limt15+v(t), if the speed of processor during the period 19962010 is provided as function of time (t) as v(t)={400t2200  if 6t<153800             if 15t20 and also interpret the answer.

Explanation

Given Information:

The speed of processor, in megahertz (MHz) during the period 19962010 is approximated as function of time (t) as v(t)={400t2200  if 6t<153800             if 15t20

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxaf(x) exists and f(a) is defined, then

limxaf(x)=f(a)

Calculation:

Consider the function v(t)={400t2200  if 6t<153800             if 15t20.

Consider the right limit:

The closed-form function 3800 exists when t15

(b)

To determine

Whether the function v(t)={400t2200  if 6x<153800             if 15t20 is continuous or not at t=15 and whether there was any abrupt change in speed of processor during 19962010.

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