Question

The body surface area (BSA) of a 180 -centimeter-tall (about six-feet-tall) person is modeled by $B=0.1 \sqrt{5 w}$ where $B$ is the BSA (in square meters) and $w$ is the weight (in kilograms). Use differentials to approximate the change in the person's BSA when the person's weight changes from 90 kilograms to 95 kilograms.

Name: Problem 43, Chapter 3: Calculus an Applied Approach
Uploaded: 2021-08-04T17:19:33-08:00
Duration: 1 min 11 s
Channel: Carson Merrill
Description: The body surface area (BSA) of a 180 -centimeter-tall (about six-feet-tall) person is modeled by B=0.1 √(5 w) where B is the BSA (in square meters) and w is the weight (in kilograms). Use differentials to approximate the change in the person's BSA when the person's weight changes from 90 kilograms to 95 kilograms.

   The body surface area (BSA) of a 180 -centimeter-tall (about six-feet-tall) person is modeled by
$B=0.1 \sqrt{5 w}$
where $B$ is the BSA (in square meters) and $w$ is the weight (in kilograms). Use differentials to approximate the change in the person's BSA when the person's weight changes from 90 kilograms to 95 kilograms.

Calculus an Applied Approach

Ron Larson, David C,… 8th Edition

Chapter 3, Problem 43

Instant Answer

Solved by Expert Carson Merrill

08/04/2021

Step 1

The function is $B=0.1 \sqrt{5w}$, which can be rewritten as $B=0.1(5w)^{1/2}$. Show more…

Show all steps

Thanks for your feedback!

The body surface area (BSA) of a 180 -centimeter-tall (about six-feet-tall) person is modeled by $B=0.1 \sqrt{5 w}$ where $B$ is the BSA (in square meters) and $w$ is the weight (in kilograms). Use differentials to approximate the change in the person's BSA when the person's weight changes from 90 kilograms to 95 kilograms.

Play audio

Feedback

Carson Merrill and 53 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Differentials

Differentials are a tool in calculus used to approximate how a small change in an independent variable affects the value of a function. By computing the derivative, we can multiply it by a small change to estimate the corresponding change in the dependent variable.

Derivative

The derivative of a function quantifies its instantaneous rate of change with respect to one of its variables. It is a fundamental concept in calculus that provides the slope of the tangent line to the function at any point, and it is crucial for using differentials in approximations.

Linear Approximation

Linear approximation is a method for estimating the value of a function near a point using the tangent line at that point. This technique relies on the derivative to create a linear model that closely represents the behavior of the function for small deviations from the point, providing an easy way to estimate changes without calculating the exact function value.

Please give Ace some feedback