   Chapter 9.1, Problem 59E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Productivity During an 8-hour shift, the rate of change of productivity (in units per hour) of infant activity centers assembled after t hours on the job is r ( t ) = 128 ( t 2 + 6 t ) ( t 2 + 6 t + 18 ) 2 , 0 ≤ t ≤ 8 (a) Find lim t → 4 r ( t ) .(b) Find lim t → 8 − r ( t ) .(c) Is the rate of productivity higher near the lunch break (at t = 4) or near quitting time (at t = 8)?

(a)

To determine

To calculate: The value of the limit limt4r(t), where r(t)=128(t2+6t)(t2+6t+18)2.

Explanation

Given Information:

The limit is limt4r(t). During an 8-hour shift, the rate of change of productivity (in units per hour) of infant activity centers assembled after t hours on the job is r(t)=128(t2+6t)(t2+6t+18)2, where 0t8.

Formula used:

For a polynomial function f(x)=anxn+an1xn1++a1x+a0 where an0 and n is a positive integer,

limxcf(x)=f(c)

This is defined for all values of c.

Calculation:

Consider the provided limit,

limt4r(t)

Substitute 128(t2+6t)(t2+6t+18)2 for r(t),

limt4r(t)=limt4(

(b)

To determine

To calculate: The value of the limit limt8r(t) where r(t)=128(t2+6t)(t2+6t+18)2.

(c)

To determine

Whether the rate of productivity higher near the lunch break (at t=4) or near quitting time (at t=8).

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