How would a small change in your average gas mileage (in miles/gallon)change the number of gallons of gas you use per month?More specifically, do the following:(a) Give numerical evidence that supports or refutes the claim that a smallchange in your average gas mileage results in an approrimately small changein the number of gallons of gas you use each month. Choose the distance youdrive each month (and keep this constant) and then at least two significantlydifferent values for the average gas mileage. Approrimate the proportionalityconstant in each case (if it erists) and write the proportionality approxima-tions. Be sure to define the appropriate variables and pay particular attentionto units.(b) Using your results from part (a), approximate the proportionality con-stants that relate the small relative change in the number of gallons of gas you use each month to a small relative change in your average gas mileage.Do this for each of the two average gas mileages you chose in part (a). Writethe proportionality relations in each case. Again, pay careful attention tounits. Do you notice anything surprising? Can you make a conjecture?(c) Now use the derivative and the appropriate linear approrimation toanalyse the questions from parts (a) and (b) in general. You can work withyour montly fixed distance, but do not assume any specific gas mileage. Thencheck the accuracy of your approrimations from parts (a) and (b). Does yourwork here confirm your conjecture? Be sure to state specific conclusions. Inparticular, can you say anything about how the relative change in the numberof gallons of gas you use each month is related to a small relative change inyour average gas mileage.Do not use differentials for the linear approximations. Use the notationof class.

Statement : A small change in your average gas mileage (in miles/gallon) change the number of…

Do you notice anything surprising? Cân you make a conjecture? (c) Now use the derivative and the appropriate linear approrimation to analyse the questions from parts (a) and (b) in general. You can work with your montly fixed distance, but do not assume any specific gas mileage. Ther check the accuracy of your approrimations from parts (a) and (b). Does you work here confirm your conjecture? Be sure to state specific conclusions. In particular, can you say anything about how the relative change in the numbe: of gallons of gas you use each month is related to a small relative change ir jour average gas mileage. Do not use differentials for the linear approximations. Use the notation

Do you notice anything surprising? Cân you make a conjecture? (c) Now use the derivative and the appropriate linear approrimation to analyse the questions from parts (a) and (b) in general. You can work with your montly fixed distance, but do not assume any specific gas mileage. Ther check the accuracy of your approrimations from parts (a) and (b). Does you work here confirm your conjecture? Be sure to state specific conclusions. In particular, can you say anything about how the relative change in the numbe: of gallons of gas you use each month is related to a small relative change ir jour average gas mileage. Do not use differentials for the linear approximations. Use the notation

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

How would a small change in your average gas mileage (in miles/gallon)
change the number of gallons of gas you use per month?
More specifically, do the following:
(a) Give numerical evidence that supports or refutes the claim that a small
change in your average gas mileage results in an approrimately small change
in the number of gallons of gas you use each month. Choose the distance you
drive each month (and keep this constant) and then at least two significantly
different values for the average gas mileage. Approrimate the proportionality
constant in each case (if it erists) and write the proportionality approxima-
tions. Be sure to define the appropriate variables and pay particular attention
to units.
(b) Using your results from part (a), approximate the proportionality con-
stants that relate the small relative change in the number of gallons of gas

you use each month to a small relative change in your average gas mileage.
Do this for each of the two average gas mileages you chose in part (a). Write
the proportionality relations in each case. Again, pay careful attention to
units. Do you notice anything surprising? Can you make a conjecture?
(c) Now use the derivative and the appropriate linear approrimation to
analyse the questions from parts (a) and (b) in general. You can work with
your montly fixed distance, but do not assume any specific gas mileage. Then
check the accuracy of your approrimations from parts (a) and (b). Does your
work here confirm your conjecture? Be sure to state specific conclusions. In
particular, can you say anything about how the relative change in the number
of gallons of gas you use each month is related to a small relative change in
your average gas mileage.
Do not use differentials for the linear approximations. Use the notation
of class.

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