TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
![Now, Let g(x) = f(x,y)dy. Then take u = b(x), v= a (x)
a(x)
и
9 (x₁ 4₁ 10) = [ f(x,y)dy by the chain Rule
v
Write
we have
b(x)
9₁₂, (2, 4, 2) = 9₁ (du) + 9₁₂ (du) + f₂ dy
dx
19
u
f (x4) u(x) = g(x, 4). 2²(x) + ] £x dy
=
V
In our example,
u(x) = 2,
u'(x) = 1
We
v(x)=0, f(x, y) = f(x,y), 9 (x) =
vel (x) = 0
x
from Ⓒ
dx [ f(x,y) dy = f(x,x) 1+ 0 + ( of (ay) dy
can write
= f(xix) + ( " of (x.y) dy
2x
*
f(x,y)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04e69fc8-7342-4555-9b13-effc35ae08ea%2Ff2d074a4-80bc-4538-9962-2878b0eafed7%2Fjq1t5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Now, Let g(x) = f(x,y)dy. Then take u = b(x), v= a (x)
a(x)
и
9 (x₁ 4₁ 10) = [ f(x,y)dy by the chain Rule
v
Write
we have
b(x)
9₁₂, (2, 4, 2) = 9₁ (du) + 9₁₂ (du) + f₂ dy
dx
19
u
f (x4) u(x) = g(x, 4). 2²(x) + ] £x dy
=
V
In our example,
u(x) = 2,
u'(x) = 1
We
v(x)=0, f(x, y) = f(x,y), 9 (x) =
vel (x) = 0
x
from Ⓒ
dx [ f(x,y) dy = f(x,x) 1+ 0 + ( of (ay) dy
can write
= f(xix) + ( " of (x.y) dy
2x
*
f(x,y)
![The tangent plane at the graphs of f(x,y) = x²ty² at (0,0)
is given by.
af
z = f(0,0) + f (x-0) + 2/3 | ₁0 (4-0)
ay
2 = 0 + 0 (0) to
⇒2=0]
is the tangent plane
Also For g(x,y)=x²³y² + xy ²³ the tangent plane at (0,0) is,
7= 9(0,0) + 3 / 2² / ₁0,00
ag
(x-0) + ag
(y-o)
=
0 +0+0
31
by 1 (0,0)
2=0] is the tangent plane
Since both fox) & g(x) have same tangent plane.
⇒ The graphs f(x,y) & g(x,y) are called tangents at (0,0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04e69fc8-7342-4555-9b13-effc35ae08ea%2Ff2d074a4-80bc-4538-9962-2878b0eafed7%2Frmm4yx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The tangent plane at the graphs of f(x,y) = x²ty² at (0,0)
is given by.
af
z = f(0,0) + f (x-0) + 2/3 | ₁0 (4-0)
ay
2 = 0 + 0 (0) to
⇒2=0]
is the tangent plane
Also For g(x,y)=x²³y² + xy ²³ the tangent plane at (0,0) is,
7= 9(0,0) + 3 / 2² / ₁0,00
ag
(x-0) + ag
(y-o)
=
0 +0+0
31
by 1 (0,0)
2=0] is the tangent plane
Since both fox) & g(x) have same tangent plane.
⇒ The graphs f(x,y) & g(x,y) are called tangents at (0,0).
Expert Solution
Step 1: Introduction of the given problem
Transcribing the text in digital format
Step by step
Solved in 4 steps with 21 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
