## Solution for problem 19 Chapter 13.7

# ?In Exercises 9 - 20, find an equation of the tangent plane to the surface at the given point. \(x y^{2}+3 x-z^{2}=8, \quad(1,-3,2)\)

Calculus: Early Transcendental Functions | 6th Edition

In Exercises 9 - 20, find an equation of the tangent plane to the surface at the given point.

\(x y^{2}+3 x-z^{2}=8, \quad(1,-3,2)\)

Text Transcription:

xy^2 + 3x - z^2 = 8, (1, -3, 2)

**Accepted Solution**

Step 1 of 5) Because the limit is r = 1, we cannot decide from the Ratio Test whether the series converges. When we notice that an+1>an = (2n + 2)>(2n + 1), we conclude that an+1 is always greater than an because (2n + 2)>(2n + 1) is always greater than 1. Therefore, all terms are greater than or equal to a1 = 2, and the nth term does not approach zero as nS q. The series diverges.

###### Chapter 13.7, Problem 19 is Solved

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?In Exercises 9 - 20, find an equation of the tangent plane to the surface at the given point. \(x y^{2}+3 x-z^{2}=8, \quad(1,-3,2)\)