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In: Advanced Math
Rudin Ch 4, p. 99 #7. If E ⊂ X and if f is a function...
Rudin Ch 4, p. 99 #7. If E ⊂ X and if f is a function defined on X, the restriction of f to E is the function g whose domain of definition is E, such that g(p) = f (p) for p ∈ E. Define f and g on 2 by: f (0, 0) = g(0, 0) = 0, f (x, y) = € xy 2 x 2 + y 4 , g(x, y) = € xy 2 x 2 + y 6 if (x, y) ≠ (0, 0). Prove that f is bounded on 2 , that g is unbounded in every neighborhood of (0, 0) and that f is not continuous at (0, 0); nevertheless, the restrictions of both f and g to every straight line in 2 are continuous! .Explain step by step in detal
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Show that, for any events E and F, P(E ∪ F) = P(E) + P(F) −...
Show that, for any events E and F, P(E ∪ F) = P(E) + P(F) − P(E
∩ F). Only use the probability axioms and indicate which axiom you
use where
consider the function f(x) = 1 + x3 e-.3x a. what is f'(x) b. what is f''(x)...
consider the function f(x) = 1 +
x3 e-.3x
a. what is f'(x)
b. what is f''(x)
c. what are the critical points of f(x)
d. are the critical points a local min or local max or
neither?
e. find the inflection points
f. if we define f(x) to have the domain of [2,50] compute the
global extreme of f(x) on that interval
what is the absolute maximum of the function f(x)=(e^x)/x, x>0?
what is the absolute maximum of the function f(x)=(e^x)/x,
x>0?
Analyze the function given by f(x) = (2x − x^2 )e^x . That is: find all...
Analyze the function given by f(x) = (2x − x^2 )e^x . That is:
find all x- and y-intercepts; find and classify all critical
points; find all inflection points; determine the concavity; find
any horizontal or vertical asymptotes. Finally, use this
information to graph the function.
A function is odd function if f (-x) = - f(x). A function is even function...
A function is odd function if f (-x) = - f(x). A
function is even function if f(-x) = f(x). f(x) = sin (x)
and f(x) = x are examples of odd functions and f(x) = cos x and
f(x) = e^ (-x)^2 are examples of even functions.
Give two more examples of even functions and two more examples
of odd functions.
Show that for odd functions f (x), integral of f(x)
from negative infinity to infinity = 0
if...
Find the Maclaurin series of the function f(x)=(3x2)e^−4x (f(x)=∑n=0∞cnxn)
Find the Maclaurin series of the function
f(x)=(3x2)e^−4x
(f(x)=∑n=0∞cnxn)
Let be the following probability density function f (x) = (1/3)[ e ^ {- x /...
Let be the following probability density function f (x) = (1/3)[
e ^ {- x / 3}] for 0 <x <1 and f (x) = 0 in any other
case
a) Determine the cumulative probability distribution F (X)
b) Determine the probability for P (0 <X <0.5)
7. Find the maximum and minimum of the function. f (x, y) = x^ 2 +...
7. Find the maximum and minimum of the function. f (x, y) = x^ 2
+ y^ 2 − xy − 3x − 3y on the triangle D ={(x, y)| x ≥ 0, y ≥ 0, x +
y ≤ 4}
Find f(x) for the following function. Then find f(6), f(0), and f(-7). f(x)=-2x^2+1x f(x)= f(6)= f(0)=...
Find f(x) for the following function. Then find f(6), f(0), and
f(-7).
f(x)=-2x^2+1x
f(x)=
f(6)=
f(0)=
f(-7)=
7. Let E be a finite extension of the field F of prime characteristic p. Show...
7. Let E be a finite extension of the field F of prime
characteristic p. Show that the
extension is separable if and only if E = F(Ep).
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