6. Find F' and dF[a; h] where: In ¤1 (a) F(x1,x2) and hence show that if v is tangent to the curve parametrized x, cos x1 by r(t) then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at F(r(t)), by direct calculation; x - 1 (b) F(x, y, z) = | and hence show that if v is tangent to the curve parametrized xy 1+z² by r(t) = t2 then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at F(r(t)), by direct calculation.
6. Find F' and dF[a; h] where: In ¤1 (a) F(x1,x2) and hence show that if v is tangent to the curve parametrized x, cos x1 by r(t) then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at F(r(t)), by direct calculation; x - 1 (b) F(x, y, z) = | and hence show that if v is tangent to the curve parametrized xy 1+z² by r(t) = t2 then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at F(r(t)), by direct calculation.
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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![6. Find F' and dF[a; h] where:
In ¤1
(a) F(x1, 22) =
and hence show that if v is tangent to the curve parametrized
x, cos x1
r(t) = [:
by
then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at
F(r(t)), by direct calculation;
х — 1
(b) F(z, y, =) =
and hence show that if v is tangent to the curve parametrized
xy
1+z2
by r(t) :
then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at
F(r(t)), by direct calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc77d576e-0319-4636-bc5a-173808e3c84b%2F552b0e48-e0a8-490c-b146-59d3923cf614%2Fgskx765_processed.png&w=3840&q=75)
Transcribed Image Text:6. Find F' and dF[a; h] where:
In ¤1
(a) F(x1, 22) =
and hence show that if v is tangent to the curve parametrized
x, cos x1
r(t) = [:
by
then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at
F(r(t)), by direct calculation;
х — 1
(b) F(z, y, =) =
and hence show that if v is tangent to the curve parametrized
xy
1+z2
by r(t) :
then dF[r(t); v] is tangent to the curve parametrized by F(r(t)) at
F(r(t)), by direct calculation.
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