CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS d. Determine the equation of the tangent line of the trace that in the previous part with y = 1 (in the z direction) at the point zo = 1. you sketched 6 6 I 0.5 Z 0.5 y 1.5 0.5 Figure 10.4.2 The traces of f(x, y) and the tangent plane. 1.5 I 0.5 68 z e. Figure 10.4.2 shows the traces of the function and the traces of the tan- gent plane. Explain how the tangent line of the trace of f, whose equation you found in the last part of this activity, is related to the tangent plane. How does this observation help you determine the constant a in the equa- tion for the tangent plane z = zo+a(z-zo)+b(y-yo)? (Hint: How do you think fz(zo, yo) should be related to zz (zo, yo)?) = f. In a similar way to what you did in (d), determine the equation of the tangent line of the trace with z = 1 at the point yo 1. Explain how this tangent line is related to the tangent plane, and use this observation to determine the constant b in the equation for the tangent plane z = zo+a(z-zo)+b(y-yo). (Hint: How do you think fy(ro, yo) should be related to zy (zo, yo)?)

CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS d. Determine the equation of the tangent line of the trace that in the previous part with y = 1 (in the z direction) at the point zo = 1. you sketched 6 6 I 0.5 Z 0.5 y 1.5 0.5 Figure 10.4.2 The traces of f(x, y) and the tangent plane. 1.5 I 0.5 68 z e. Figure 10.4.2 shows the traces of the function and the traces of the tan- gent plane. Explain how the tangent line of the trace of f, whose equation you found in the last part of this activity, is related to the tangent plane. How does this observation help you determine the constant a in the equa- tion for the tangent plane z = zo+a(z-zo)+b(y-yo)? (Hint: How do you think fz(zo, yo) should be related to zz (zo, yo)?) = f. In a similar way to what you did in (d), determine the equation of the tangent line of the trace with z = 1 at the point yo 1. Explain how this tangent line is related to the tangent plane, and use this observation to determine the constant b in the equation for the tangent plane z = zo+a(z-zo)+b(y-yo). (Hint: How do you think fy(ro, yo) should be related to zy (zo, yo)?)

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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