Question
In: Advanced Math
NOTE- If it is true, you need to prove it and If it is false, give...
NOTE- If it is true, you need to prove it and If it is false, give a counterexample
f : [a, b] → R is continuous and in the open interval (a,b) differentiable.
a) If f(a) ≥ f(b), then exists a ξ ∈ (a,b) with f′(ξ) ≤ 0. (TRUE or FALSE?)
b) If f is reversable, then f −1 differentiable. (TRUE or FALSE?)
c) f is constant ⇐⇒ ∀x∈(a,b): f′(x)=0 (TRUE or FALSE?)
Solutions
Colby Messinger answered 1 year agoRelated Solutions
NOTE- If it is true, you need to prove it and If it is false, give...
NOTE- If it is true, you need to prove it and If it is false,
give a counterexample
f : [a, b] → R is continuous and in the open interval (a,b)
differentiable.
a) If f(a) ≥ f(b), then exists a ξ ∈ (a,b) with f′(ξ) ≤ 0.(TRUE
or FALSE?)
b) If f is reversable, then f −1 differentiable. (TRUE or
FALSE?)
c) If f ′ is limited, then f is lipschitz. (TRUE or FALSE?)
Determine whether each statement is true or false. If it is true, prove it. If it...
Determine whether each statement is true or false. If it is
true, prove it. If it is false, give a counterexample.
a) For every function f : X → Y and all A ⊆ X, we have f^−1
[f[A]] = A.
(b) For every function f : X → Y and all A ⊆ X, we have f[X \ A]
= Y \ f[A].
(c) For every function f : X → Y and all A, B ⊆ Y ,...
(need in frame -c) In the given code, Will all the assert statements prove true? Give...
(need in frame -c)
In the given code,
Will all the assert statements prove true? Give reason for
proved
true or false for each assert statement. [3 M] [CO2]
int main(){
int i = 1;
int x = 33;
/*@
loop invariant 1 <= i <= 19;
loop assigns i;
loop variant 20 - i;
*/
//@assert i == 1;
while(i < 20){
++i;
if(i == 20) break ;
}
//@assert i == 20;
//@assert x == 33;
}
frama-c...
1. Determine if the following statements are true or false. If a statement is true, prove...
1. Determine if the following statements are true or false. If a
statement is true, prove it in general, If a statement is false,
provide a specific counterexample.
Let V and W be finite-dimensional vector spaces over field F,
and let φ: V → W be a linear transformation.
A) If φ is injective, then dim(V) ≤ dim(W).
B) If dim(V) ≤ dim(W), then φ is injective.
C) If φ is surjective, then dim(V) ≥ dim(W).
D) If dim(V) ≥...
The following are True or False statements. If True, give a simple justification. If False, justify,...
The following are True
or False statements. If True, give a simple justification. If False,
justify, or better, give a counterexample.
1. (R,discrete) is a
complete metric space.
2. (Q,discrete) is a compact metric space.
3. Every continuous function from R to R maps an interval to an
interval.
4. The set {(x,y,z) :
x2 −y3 + sin(xy) < 2} is open in
R3
Indicate whether the statement is true or false. If false, please explain why. (Note that if...
Indicate whether the statement is true or false. If false,
please explain why. (Note that if the explanation is incomplete,
you may not get the full credits.)
a. Although payroll taxes are imposed on firms, workers bear
more burdens than firms when the elasticity of labor supply is
greater than the elasticity of labor demand. (4 pts)
b. There might be a situation in which dangerous jobs offer
lower wages than safe jobs even if there exist compensating wage
differentials....
This is true and false and if the asnwer is false i need the correct answer....
This is true and false and if the asnwer is false i need the
correct answer.
_____ The least squares slope for predicting y from
x is the same asthe least squares slope for predicting
xfrom y
_____ The least squares linepasses through the point of averages
.
_____ A residual is the deviation of a point from the point of
averages
_____ It is common to use a residual plotbased on plotting the
residuals versus x.
______Theleast squares lineis...
True or False. Please give an explanation as to why its true or false. Too much...
True or False. Please give an explanation as to why its true or
false.
Too much leverage on a company’s balance sheet will increase the
company’s cost of equity/
Write a formal proof to prove the following conjecture to be true or false. If the...
Write a formal proof to prove the following conjecture to be
true or false.
If the statement is true, write a formal proof of it. If the
statement is false, provide a counterexample and a slightly
modified statement that is true and write a formal proof of your
new statement.
Conjecture: Let w, x, y, and z be single-digit numbers. The
4-digit number wxyz* is divisible by 9 if and only if 9 divides the
sum w + x +...
Determine whether the statement is true or false. If it is false, explain why or give...
Determine whether the statement is true or false. If it is
false, explain why or give an example that shows it is false.
If f(c) = L,then lim x→c f(x) = L.
False. Define f to be the piece-wise function where
f(x) = x + 3 when x ≠ −1 and
f(x) = 2 when x = −1. Then we have
f(−1) = 2 while the limit of f as x
approaches −1 is equal to −2.
False. Define f...
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