2011年12月8日 · Assume that f is a differentiable function such that f(0)=f'(0)=0 and f''(0)>0. Argue that there exists a positive constant a>0 such that f(x)>0 for all x in the interval (0,a). Can anything be concluded about f(x) for negative x's? Homework Equations The Attempt at a Solution I think I should use the MVT so here is what I tried:

2008年11月15日 · Since f(x) and that are exactly the same for all x except x= 0, they have the same limit at x=0. What is the limit as x goes to 0? Define f(0) to be that limit.

2014年7月10日 · F = 0 implies the system's forces are in equilibrium, or that every action has an equal and opposite reaction. This means the system is not being acted on by any outside forces and is either at rest, or moving with CONSTANT velocity (If you have any calculus background you know that a = [itex]\frac{dv}{dt}[/itex], and that the derivative of a ...

2012年4月4日 · If you know about exterior derivatives, then this identity is equivalent to [itex]d^2 = 0[/itex]. To give a "physical picture" for this identity, first use Gauss's Theorem for [itex]\mathrm{div}(\mathrm{curl} \, \vec{F})[/itex] to get:

So f(0) = 230/9 = 25.6 to the nearest tenth. (2) As in a huge number of other applications, f(0) means an initial value. It's not part of your question, but another important number in a logistic function is the carrying capacity, which is the limit of the function value as x gets very large.

2025年2月4日 · A continuous function is one that you can draw in one line without interception, roughly speaking. So if we have a point ##(a,f(a))## with ##f(a)>0 ## and a point ##(b,f(b))## with ##f(b)<0## then the line that represents the function, i.e. its graph, has to cross the ##x##-axis at some point ##x=c## and there we have ##f(c)=0,## if …

2025年3月4日 · My solution: Let ##f(x+y)=f(x)f(y)-[f(x)+f(y)]-1/2## İf ##y=x## we find functional equation that given us. So for ##x=y=1## then ##f(2)=-1/2## İf we evaluate ##x=1, y=2## at above equation ##f(3)=-3## My question is: What is the solution of that functional equation; I mean are there other...

2009年2月3日 · If f(x_0)=c and c > 0 then the function must go up to atleast c, and since it is continuous it does not "jump" there. I was thinking of making a small partition of a,x_0, and b. I then know what the sup or inf values of the two rectangles (speaking of the hieghts) will be greater than or equal to x_0 for the upper sum.

2024年12月15日 · ##F_a=\frac 12(f_0\frac{c+v}{c-v}-f_0)=f_0\frac{v}{c-v}## in agreement with the official answer. The ‘beat frequency’ is in fact ##2F_a## corresponding to your answer. That’s where the confusion arose. You need to think about why this is so! Minor edit.

2025年3月6日 · ##M a_{cm} = F_{ext}## Hi, I started this thread to address the solution of this problem. ProblemView attachment 358160 A yo-yo of radii ##R_1=R## and ##R_2=\frac{7}{5}R## is acted upon by forces ##F## and ##\kappa F~~~(0<\kappa<\infty)## as shown in the figure on the right. The yo-yo rolls without slipping on the horizontal surface.