What is decreasing: Definition and 205 Discussions
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
As a follow up for : https://www.physicsforums.com/threads/let-k-n-show-that-there-is-i-n-s-t-1-1-k-i-1-2-k-i-1-4.1054669/
show that ## \alpha\left(k\right)\ :=\ \left(1-\tfrac{1}{k}\right)^{\ln\left(2\right)k}-\left(1-\tfrac{2}{k}\right)^{\ln\left(2\right)k} ## is decreasing for ##...
Please walk me step by step on how to do it (we don't have imaginary numbers so don't bring that up)
Also how to put signs on the numbers line when I get minus in the root? (non solveable equation)
Sorry for my English.
For this,
I first try to work out where function is increasing
My working is
##f'(x) = 12x^3 - 12x^2 - 24x##
For increasing,
##12x(x^2 - x - 2) > 0##
##12x > 0## and ##(x - 2)(x + 1) > 0##
##x > 0## and ##x > 2## and ##x > -1##
However, how do I combine those facts into a single domain...
The answer key states that the new tangential speed is half the original speed. However, this isn't correct right? It should double.
My proof:
##F_c = \frac {mv^2} R##
##F_c = F_t##
##\frac {mv^2} {\frac R 4} = \frac {m(2v)^2} R## If centripetal force were to stay constant.
As such, tangential...
I don't understand part (c) the answer is decreasing for both. I would have it decreasing for the centripetal acceleration and then increasing for the velocity, why is that not correct?
Thanks in advance!
What are intervals of which the function $g(t)=3t^2-5t+1$
a. find the vertex convert to vertex form $g(t)=a(t-h)^2-k$
\item $g(t)=3\left(t-\dfrac{5}{3}t+\left(\dfrac{5}{6}\right)^2\right)
+1-\dfrac{25}{12}
=3\left(t-\dfrac{5}{6}\right)^2-\dfrac{13}{12}$
b. the parabola opens up and the vertex is...
Hello, I don't know to solve this exercise:
Let $\mathcal{B}_\mathbb{R}$ the $\sigma-algebra$ Borel in $\mathbb{R}$ and let $\mu : \mathcal{B}_\mathbb{R} \rightarrow{} \mathbb{R}_{+}$ a finite measure. For each $x \in \mathbb{R}$ define
$$f_{\mu} := \mu((- \infty,x]) $$
Prove that:
a)...
Problem: Find the cardinality of the set ## A = \{f \in \Bbb N \to \Bbb N. \forall n\leq m .f(n) \geq f (m) \} ##.
I know that ## A \subseteq P(\Bbb N \times \Bbb N) ## implies ## |A| \leq |P(\Bbb N \times \Bbb N)| = | P(\Bbb N) | = \aleph ##. So I have a feeling that ## \aleph \leq |A| ##...
When she is stacking ##5## rings, then there are ##5P5## configurations when it comes to arranging rings, and each configuration can be arranged on her fingers in ##5P1## ways (choose one finger from 5 to put that configuration on).
When she is stacking ##4## rings, then we have two objects; a...
CV19 infection numbers are increasing substantially throughout the world, but deaths from the virus are steadily decreasing, why is this?
Does this mean that the virus is becoming less virulent?
Hello,
I want to know what is the incresing and decreasing interval of this even function $|e^x+e^{-x}|?$
If any member knows the correct answer, may reply to this question.
I am developing a market trade bot and need to extract some parameters from market data but I don't have idea how to do it exactly. need your help.
1) How to reproduce if market is increasing or decreasing at certain point? (ex. see below picture)
2) Does exist any formula how to reproduce...
hi,
I'm working on a rotational system, and my goal is to rotate a 500kg(1100lbs) load to 90° in 1.5 seconds. Inertia of load makes system hard to accelerate and decelerate. I designed a gear system but still motor needs too much torque.
Is there any possible method to decrease motor torque...
Why when we supply energy for biological body then the body can keep entropy not increase?Because we know that by definition temperature equals partial derivative of internal energy to entropy.So that when temperature being constant,if internal energy increase(supplying energy for body) then...
I assumed that the same magnitude of force acts on all sides of the box. Since A had the smallest area, I ranked P(A) as having the largest pressure, followed by P(B) having the second largest and P(top) and P(bottom) having the same pressure at third largest each. However, the ranking I...
how to write a summation with decreasing index
say for adding from index 1 to n for $x_k$ we write $\sum^{n}_{k=1}x_k$.
how do we write the above for index to go from n to 1 down wards
Homework Statement
If a man of height 6ft moves with 5ft/sec velocity towards a lamp hanging at 15ft height, then at what rate his shadow will decrease?
Homework Equations
Not sure but dynamic equations can help.
The Attempt at a Solution
I have no idea about how I can approach.So I want some...
I'm reading a proof, and it says that since ##\lim_{n\to\infty}a_n = 0## and ##a_{n+1}\le a_n## for all ##n##, it must be the case that ##a_n \ge 0##.
This seems very obvious, since if ##a_n < 0## for some ##n## then it would decreasing from then on, so there wouldn't be infinitely many...
Homework Statement
Prove that if ##(a_n)## is a decreasing sequence of positive numbers and ##\sum a_n## converges, then ##\lim na_n = 0##
Homework EquationsThe Attempt at a Solution
Let ##\epsilon >0##. By the Cauchy criterion there exists an ##N\in \mathbb{N}## such that ##\forall n\ge m\ge...
I assume that before the Big Bang, there was no Higgs Field, since there was no universe for it to fill.
I assume that at the moment of the Big Bang, it began to seep into every corner of the expanding universe and was carried by inflation, that is, moving faster than the speed of light by the...
Let ##M## be a left R-module and ##f:M \to M## an R-endomorphism.
Consider this infinite descending sequence of submodules of ##M##
##M \supseteq f(M) \supseteq f^2(M) \supseteq f^3(M) \supseteq \cdots (1)##
Can anybody show that the sequence (1) is strictly descending if ##f## is injective...
Homework Statement
decreasing the resistance increases the current if the voltage remains unchanged.
Homework Equations
V=IR
The Attempt at a Solution
The solution in the book does not count this as a true statement, but it seems true to me. Is there any reason why the statement would be false?
Homework Statement
Hi everyone,
8th grade physics teacher here.
We are doing a handout where we have to identify time-velocity graphs with descriptions. Can you help me with this one?
https://imgur.com/a/vEIkg
A) The velocity is increasing at a uniform rate.
B) The velocity is decreasing at...
So I've been stuck on trying to figure out the following problem. This is basically just for my own interest, not for a school problem or anything like that. It came out of trying to get my head around Poisson and exponential distributions.
Imagine you have a process where you have a fixed...
Homework Statement
Hi everyone,
8th grade physics teacher here.
We are doing a handout where we have to identify time-velocity graphs with descriptions. Can you help me with this one?
https://imgur.com/a/vEIkg
A) The velocity is increasing at a uniform rate.
B) The velocity is decreasing at...
Hiya everyone,
Alright ?
I have a simple theoretical question. In a decreasing geometric series, is it true to say that the ratio q has to be 0<q<1, assuming that all members of the series are positive ? What if they weren't all positive ?
Thank you in advance !
Homework Statement
f(x)=x[ax-x^2]^ (1/2) for a>0
Then,f(x)
A)increases on (3a/4 , a)
B)decreases on (0, 3a/4)
C)both A,B
D)None of these
Homework Equations
differentiation chain rule
f(x) is said to be increasing in (a,b) if it's derivative is positive and decreasing if it's derivative is...
If the air resistance causes a vertical retardation of 10 percent of value of acceleration due to gravity, then the time of flight of a projectile will be decreased by nearly? Take g=10m/s^2
My attempt: Only the vertical component of the projectile will be affected by changes in g
I understand...
Hello! I have an issue with the power density of a 488 nm continuous wave laser. I'm using this laser to excite my sample. The problem is that even at low power, the laser is causing the samples to form a burn deposit on the quartz sample holder. Between the laser source and the sample, there...
Hi, So I am working with measurements using a laser. What I have noticed is that the power of the laser decreases from the time we start the laser until maybe an hour later.
Today I noticed it has decreased 10%, from yesterday, which I think sounds like a lot.
Does the laser have to warm up and...
Homework Statement
A mass ##m## whirls around on a string which passes through a ring. Given that gravity is not present and initially the mass is at a distance ##r_0## from the center and is revolving at angular velocity ##\omega_0##. The string is pulled with constant velocity ##V## starting...
Why is it so much easier to increase the temperature of something than it is to decrease the temperature?
Why are refrigerators more complex than stoves?
In my experiments, on a flat plane, when I incrementally increase the normal force acting on a rubber block, I am measuring a decrease in the static coefficient of friction. I am also measuring the friction force, which increases as normal force increases BUT this is not a proportional increase...
Homework Statement
I am trying to understand the law of conservation of energy from a very general perspective but coming across some issues. I am using the equation mentioned at end of this post, which is true for a system with no heat flows into or out of the system.
In two situations...
Hi, I have a question about taylor polynomials.
https://wikimedia.org/api/rest_v1/media/math/render/svg/09523585d1633ee9c48750c11b60d82c82b315bfI was looking for proof that why every lagrange remainder is decreasing as the order of lagnrange remainder increases.
so on wikipedia, it says, for a...
Hello !
I am currently investigating a technique that would allow several spark gaps to breakdown synchronously in an enclosed but not hermetical cavity, flushed with N2 at 1atm and ~25°C
My idea was to use "indirect" photoionization (basically a synthetic fused quartz UV flash discharge inside...
i want to know if any real function can be expressed as:
f(x)=g(x)+h(x) such as g(x) is an increasing function and h(x) is a decreasing function?
thanks
Homework Statement
Imagine a interference pattern like the common water-wave interference pattern.
What effect would decreasing the distance between the 2 wave sources have on the interference pattern?
Homework EquationsThe Attempt at a Solution
A change in the distance between the two...
Homework Statement
I am trying to show that ##n^{1/n}## is monotonically decreasing for ##n \ge 3##.
Homework EquationsThe Attempt at a Solution
I am trying to prove the claim using induction. The base case is involves a trivial calculation. What I am having trouble is the induction step...
Homework Statement
A stationary, axisymmetric, spacetime has two Killing vector fields [ξt, ξφ] corresponding to translation along t or φ directions. A particle of unit mass moving in this spacetime has a four-velocity u = γ[ξt + Ωξφ].
(i) Explain why we can interpret this as a particle moving...
I want to detect whether potentiometer output voltage is increasing or decreasing and convert this to a digital signal.
the circuit must be able to sense tiny voltage changes (order of 10mV) and with high speed.
all I am interested is if Vout increases or decreases not by how much
increasing V...
If there is enough gravity and the universe starts to collapse in on itself, would life forms that live during this phase of the universe get younger as time passes and they would need to expend energy to stay old?
Is it always true that if I have any system of resistors and I calculate the resistance between two points, when I decrease the resistance of one resistor, then the resistance measured between the same two points as previously will not increase?
I.E if i have lots of resistors between two...