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h(x, y, z) = x sin(x + 2y + 3z) P be the point (π, 7, 0) Find kER such that P lies on the level set A: h(x, y, z) = k Find a formula for the plane tangent to A at P

h(x, y, z) = x sin(x + 2y + 3z) P be the point (π, 7, 0) Find kER such that P lies on the level set A: h(x, y, z) = k Find a formula for the plane tangent to A at P

Advanced Engineering Mathematics
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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### Problem Statement Given the function: \[ h(x, y, z) = x \sin(x + 2y + 3z) \] Let \( P \) be the point \( (\pi, \pi, 0) \). 1. **Find \( k \in \mathbb{R} \) such that \( P \) lies on the level set** \[ \Lambda : h(x, y, z) = k \] 2. **Find a formula for the plane tangent to \( \Lambda \) at \( P \).**
Transcribed Image Text:### Problem Statement Given the function: \[ h(x, y, z) = x \sin(x + 2y + 3z) \] Let \( P \) be the point \( (\pi, \pi, 0) \). 1. **Find \( k \in \mathbb{R} \) such that \( P \) lies on the level set** \[ \Lambda : h(x, y, z) = k \] 2. **Find a formula for the plane tangent to \( \Lambda \) at \( P \).**
Expert Solution
Step 1: Writing down the given information

Given the function h open parentheses x comma y comma z close parentheses equals x sin open parentheses x plus 2 y plus 3 z close parentheses and the point P open parentheses pi comma pi comma 0 close parentheses.

Consider the level set capital lambda colon h open parentheses x comma y comma z close parentheses equals k.

We need to find k∈R such that h(π,π,0)=k.

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