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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

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 1970–2000 can be approximated by the following function of time t in years since the start of 1970:

v ( t ) = { 3 t                        if 0 t < 20 174 t 3 , 420       if 20 t 30.

a. Compute lim t 20 v ( t )

and lim t 20 + v ( t ) , and interpret each answer.

b. Is the function v continuous at t = 20 ? According to the model, was there any abrupt change in processor speeds during the period 1970–2000?

(a)

To determine

To calculate: The limits limt20v(t) and limt20+v(t), if the speed of processor during the period 19702000 is approximated by a function of time (t) as v(t)={3t                 if 0t<20174t3420  if 20t30 and also interpret the answer.

Explanation

Given Information:

The speed of a processor during the period 19702000 is approximated by a function of time (t) as v(t)={3t                 if 0t<20174t3420  if 20t30

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)={3t                 if 0t<20174t3420  if 20t30.

Consider the right limit:

The closed-form function 174t3420 exists when t20

(b)

To determine

Whether the function v(t)={3t                 if 0t<20174t3420  if 20t30 is continuous or not at t=20 and whether there was any abrupt change in speed of processor during 19702000.

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