solve the question 6 with complete explanation asap 6. Consider the sphere a? + y? + (z - 3)2 = 1. Find the point P (a, b, c) on the spheresuch that the tangent plane to the sphere at P intersects the ry-plane in the liney = 3x.7. Let V be a vector space and l: V →R be a linear map. If z E V is not in the nullspaceof €, show that every r EV can be decomposed uniquely as r = v+cz , where v E Vis in the nullspace of l and c ER is a scalar.8. Consider the three functions a(r), b(x), and c(r) given by:3n3n+1a(x) = E(3n)!b(1x) = E;3n+2-Σc(x)(Зп + 1)!(Зп + 2)!n=0n=0n=0(a) Determine the radius of convergence for each of function.(b) Give a formula for the nth derivative a(n) (r) for all n E N.

Answered: Image /qna-images/answer/807b864f-55dd-40b6-9c09-d142239bf098.jpg

Answered: 6. Consider the sphere a2 + y? + (z-3)2…

6. Consider the sphere a2 + y? + (z-3)2 = 1. Find the point P (a, b, c) on the sphere such that the tangent plane to the sphere at P intersects the ry-plane in the line y = 3x.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

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Question

solve the question 6 with complete explanation asap

6. Consider the sphere a? + y? + (z - 3)2 = 1. Find the point P (a, b, c) on the sphere
such that the tangent plane to the sphere at P intersects the ry-plane in the line
y = 3x.
7. Let V be a vector space and l: V →R be a linear map. If z E V is not in the nullspace
of €, show that every r EV can be decomposed uniquely as r = v+cz , where v E V
is in the nullspace of l and c ER is a scalar.
8. Consider the three functions a(r), b(x), and c(r) given by:
3n
3n+1
a(x) = E
(3n)!
b(1x) = E;
3n+2
-Σ
c(x)
(Зп + 1)!
(Зп + 2)!
n=0
n=0
n=0
(a) Determine the radius of convergence for each of function.
(b) Give a formula for the nth derivative a(n) (r) for all n E N.

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