√ (Use decimal notation. Give your answer to four decimal places.) Use the Linear Approximation to f(x, y) = 81.1 15.9 at (81, 16) to estimate 81.1 15.9
√ (Use decimal notation. Give your answer to four decimal places.) Use the Linear Approximation to f(x, y) = 81.1 15.9 at (81, 16) to estimate 81.1 15.9
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Use the Linear Approximation to \( f(x, y) = \sqrt{\frac{x}{y}} \) at \( (81, 16) \) to estimate \( \sqrt{\frac{81.1}{15.9}} \).
(Use decimal notation. Give your answer to four decimal places.)
\[
\sqrt{\frac{81.1}{15.9}} \approx \underline{\hspace{4cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F646bd109-e2a6-4c6a-a3ea-1fdf7467c156%2Fc9f1fd48-a45e-45c7-9869-7f65bb330122%2Fthwe97j_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Use the Linear Approximation to \( f(x, y) = \sqrt{\frac{x}{y}} \) at \( (81, 16) \) to estimate \( \sqrt{\frac{81.1}{15.9}} \).
(Use decimal notation. Give your answer to four decimal places.)
\[
\sqrt{\frac{81.1}{15.9}} \approx \underline{\hspace{4cm}}
\]
Expert Solution
Step 1
Given:
To find:
The linear approximation for at the point .
Formula to find the linear approximation for the function :
.
where, and are the partial derivatives of the function with respect to and respectively.
Differentiation Formula:
.
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
