3. Use grad h(-3,4)=5ī +3j and h(-3,4)=10 to answer the following questions. a) Find the differential of h at (-3,4). b) Find a normal vector to the contour of h at (−3,4). c) Find an equation of a tangent line to the contour of h at (-3,4). d) Find a normal vector to the surface of h at (-3,4,10). e) Find an equation of a tangent plane to the graph of h at (-3,4,10).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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3. Use grad h(-3,4)=5i +3j and h(-3,4)=10 to answer the following questions.
a) Find the differential of h at (-3,4).
b) Find a normal vector to the contour of h at (-3,4).
c) Find an equation of a tangent line to the contour of h at (-3,4).
d) Find a normal vector to the surface of h at (-3,4,10).
e) Find an equation of a tangent plane to the graph of h at (-3,4,10).
Transcribed Image Text:3. Use grad h(-3,4)=5i +3j and h(-3,4)=10 to answer the following questions. a) Find the differential of h at (-3,4). b) Find a normal vector to the contour of h at (-3,4). c) Find an equation of a tangent line to the contour of h at (-3,4). d) Find a normal vector to the surface of h at (-3,4,10). e) Find an equation of a tangent plane to the graph of h at (-3,4,10).
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