This is a table of the values of a function H(t, h) at selected values of (t, h): Įt\h→ 100 100 115.1 165.1 | 215.1 120.4 170.4| 220.4 115.9| 165.9 | 215.9 101.6 151.6 201.6 77.5 150 200 150 200 1 4 127.5 177.5 1. Determine an approximate value for at (3, 150) 2. Determine an approximate value for at (3,150) 3. Use your answers to points 1 and 2 to find an approximate value for Н(26, 156) 4. The values in the table come from the exact function H(t, h) = h + 20t – 4.9t² which gives the height in meters above the ground after t seconds of an object thrown upward from an initial height of h meters, with an initial velocity of 20 meters per second, neglecting air friction. Compare your estimates in points 1, 2, and 3 with the exact values, using the explicit form of H.

This is a table of the values of a function H(t, h) at selected values of (t, h): Įt\h→ 100 100 115.1 165.1 | 215.1 120.4 170.4| 220.4 115.9| 165.9 | 215.9 101.6 151.6 201.6 77.5 150 200 150 200 1 4 127.5 177.5 1. Determine an approximate value for at (3, 150) 2. Determine an approximate value for at (3,150) 3. Use your answers to points 1 and 2 to find an approximate value for Н(26, 156) 4. The values in the table come from the exact function H(t, h) = h + 20t – 4.9t² which gives the height in meters above the ground after t seconds of an object thrown upward from an initial height of h meters, with an initial velocity of 20 meters per second, neglecting air friction. Compare your estimates in points 1, 2, and 3 with the exact values, using the explicit form of H.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Exponential Growth Model

The relation that represents an exponential function is:

Question

This is a table of the values of a function H(t, h) at selected values of (t, h):
It\h→
100
150
200
100
150
200
165.1 215.1
170.4 220.4
115.9 | 165.9 215.9
101.6 151.6 201.6
77.5 127.5 177.5
1
115.1
2
120.4
3
4
5
1. Determine an approximate value for H at (3, 150)
2. Determine an approximate value for H at (3,150)
3. Use your answers to points 1 and 2 to find an approximate value for
Н(2.6, 156)
4. The values in the table come from the exact function
H(t, h) = h + 20t – 4.9t2
which gives the height in meters above the ground after t seconds of an
object thrown upward from an initial height of h meters, with an initial
velocity of 20 meters per second, neglecting air friction. Compare your
estimates in points 1, 2, and 3 with the exact values, using the explicit
form of H.
Note When faced with a table of discrete values for a function we clearly cannot
determine derivatives exactly, and even our approximations cannot be
complemented with an estimate of the error involved. Still, we should
reduce the inevitable bias in our estimates by using the symmetric form,
for the first derivative, f'(x) z fa+h)-f(a-h) (that's the average of the
"right" and "left" average rates of change), where x – h < x < x + h are
three neighboring data points.

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