Numeracy 2. A function of n variables f(x), where x = (x1,..., xn), is said to be homogeneous of degree kEN if f(tx) = tk f(x) for all t e R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. f(x, y, z) = Vx° + y9 + z9 2. f(x, y, z, w) = x²y² + z?w² + xyzw f(x, y) = Vr2 + y². to 3. r+y 4. Numeracy 3. Solve the following non-linear system of equations: x2 + y? + 22 = 2 2.x? + y 22 = 3
Numeracy 2. A function of n variables f(x), where x = (x1,..., xn), is said to be homogeneous of degree kEN if f(tx) = tk f(x) for all t e R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. f(x, y, z) = Vx° + y9 + z9 2. f(x, y, z, w) = x²y² + z?w² + xyzw f(x, y) = Vr2 + y². to 3. r+y 4. Numeracy 3. Solve the following non-linear system of equations: x2 + y? + 22 = 2 2.x? + y 22 = 3
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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Transcribed Image Text:Numeracy 2. A function of n variables f(x), where x (x1,..., xn), is said to be homogeneous of degree kEN if
f(tx) = tk f(x) for all t e R. For each function below, show it is homogeneous (of some degree k) or give an example
to show it is not homogeneous.
1.
f (x, y, z) = x9 + y9 + 29
2.
f (x, y, z, w)
= x?y? + z?w² + xyzw
3.
f (x, y) =
2+ y².
rr+y
4.
f (x, y)
Numeracy 3.
Solve the following non-linear system of equations:
22 + y? + 22 = 6
22 – y? + 222 = 2
2.x2 + y? – 22 = 3
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