Use a tangent plane to approximate the value of the following function at the point (-0.9, -10.1): arctan(ry +101) Present you answer accurate to four decimal places. f (x, y) L
Use a tangent plane to approximate the value of the following function at the point (-0.9, -10.1): arctan(ry +101) Present you answer accurate to four decimal places. f (x, y) L
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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![### Calculus Exercise: Approximating with a Tangent Plane
**Task:**
Use a tangent plane to approximate the value of the following function at the point \((-0.9, -10.1)\):
\[
f(x, y) = \arctan(xy^2 + 101)
\]
Present your answer accurate to four decimal places.
**Instructions:**
1. Follow the steps to find the partial derivatives of the function with respect to \(x\) and \(y\).
2. Evaluate these derivatives at the given point.
3. Use the formula for the tangent plane to approximate the desired function value.
**Note:**
- Fill in your calculated answer in the provided textbox.
- Once your calculations are complete, press "Submit Question" to check your result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a3f3121-07ef-4e2d-8122-d3ccd0e5a601%2F41ad583d-2fcb-4fb0-b41b-067e807e0991%2F8cmut7d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Exercise: Approximating with a Tangent Plane
**Task:**
Use a tangent plane to approximate the value of the following function at the point \((-0.9, -10.1)\):
\[
f(x, y) = \arctan(xy^2 + 101)
\]
Present your answer accurate to four decimal places.
**Instructions:**
1. Follow the steps to find the partial derivatives of the function with respect to \(x\) and \(y\).
2. Evaluate these derivatives at the given point.
3. Use the formula for the tangent plane to approximate the desired function value.
**Note:**
- Fill in your calculated answer in the provided textbox.
- Once your calculations are complete, press "Submit Question" to check your result.
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