/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 3 A limit representing an instanta... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q. 3 (page 151)

A limit representing an instantaneous rate of change: After t seconds, a bowling ball dropped from 350feet has height h(t)=350-16t2,measured in feet.

Take the limit as h鈫�0+of the formula you found for average rate of change in the previous problem. What does this limit represent in real-world terms?

Short Answer

Expert verified

Limit h鈫�0+represents the initial time of observation of the average rate of change in height that is-96.

Step by step solution

01

Step 1. Given information.

The given function for the height ish(t)=350-16t2.

Given limit isrole="math" localid="1649778084185" h鈫�0+

02

Step 2. The average rate of change in the height 

The average rate of change in the height of the bowling ball is as follows.

r=h(h+3)-h(3)(t+3)-3r=350-16(h+3)2-350-1632h+3-3r=350-16h2-96h-144-350+144hr=-16h2-96hhr=-16h-96

Take limit h鈫�0+for The average rate of change in the height.

limh鈫�0+r=limh鈫�0+-16h-96=-16(0)-96=-96

Limit h鈫�0+represents the initial time of observation of the average rate of change in height that is -96.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For each limit limx鈫�cf(x)=Lin Exercises 43鈥�54, use graphs and algebra to approximate the largest value of 未such that if localid="1648023101818" x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚)

localid="1648023199049" role="math" limx鈫�-1x2-2x-3x+1=-4,蔚=1

Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47鈥�60.

limx鈫�1x2-1x-1=2

State what it means for a functionf to be continuous at a point x = c, in terms of the delta鈥揺psilon definition of limit.

Write a delta鈥揺psilon proof that proves that fis continuous on its domain. In each case, you will need to assume that 未 is less than or equal to 1.

f(x)=x3
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.