How can I calculate ∂/∂t(∫01 f(x,t,H(x-t)*a)dt), where a is a constant, H(x) is the Heaviside step function, and f is
I know it must have something to do with distributions and the derivative of the Heaviside function which is ∂/∂t(H(t))=δ(x)... but I don't understand how can I work with the...
Homework Statement
Let L1 be the tangent line to r(t) at the point t = a and let L2 be the tangent line where t = b. Find the equation of the lines L1. Find the equation of the lines L1 and L2 and find the points of intersection.
r(t) = <f(t), g(t), h(t)>
*bolded letters are vectors
Homework...
Hello.
I am having a lot of trouble trying to solve/analyse this integral:
$$\displaystyle \int_2^\infty \frac{x+y}{(y)(y^2-1)(\ln(x+y))} dy$$
I have tried everything with no result; it seems impossible for me to work with that natural logarithn.
I have also tried to compute it, as it...
What does it mean for a ##f(x,y)## to be differentiable at ##(a,b)##? Do I have to somehow show ##f(x,y)-f(a,b)-\nabla f(a,b)\cdot \left( x-a,y-b \right) =0 ##? To show the function is not though, it's enough to show, using the limit definition, that the partial derivative approaching in one...
Homework Statement
I have to prove some things on the Weber-Ferma problem. Here is the assignment :
We want to find a point $$x$$ in the plane whose sum of weighted
distances from a given set of fixed points $$y_1, ...,y_m$$ is minimized.
1-Show that there exist a global mimimum to the...
If you have a function x = x(u,t)
then does u necessarily depend on x and t? so u = (x,t)
For example, if x(u,t)=u^2 t it seems that because t=x/u^2 , t=t(x,u)
I am having difficulty working out the general equation for dz \over dx if z=z(x,y,t) x=x(u,t) y=y(u,v,t)
The chain rule...
Hi everyone.
I was working on a problem for days.
The problem statement is: "Consider points P(2,1,3), Q(1,2,1), R(-1,-1,-2), S(1,-4,0). Find the shortest distance between lines PQ and RS."
Now, I did the following formula: PS dot (PQ x RS) / magnitude of (PQ x RS). (For skew lines)
Now...
Homework Statement :
the question wants me to prove that the limit of f(x,y) as x approaches 1.3 and y approaches -1 is (3.3, 4.4, 0.3). f(x,y) is defined as (2y2+x, -2x+7, x+y).
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The attempt at a solution: This is the solution my lecturer has given. it's not very neat, sorry...
T(t) = Ts+(98.6 – Ts)e-kt
rewrite in the form t=g-1(T)
In trying to understand how to find the inverse of this but am having a hard time, please advise.
Thanks,
Kupkake303
As a undergrad future scientist, in my free time I like to do some programming to get some practice as my education programme doesn't include it, but it is a useful skill to have.
I am programming some type of roguelike game, so I can get away from graphics and focus on procedural generation...
How do you find a normal vector of a function at a point, such as f(x,y)= ax^y+yx^y^x+b at (X_o,Y_o)
where a and b are just arbitrary constants, and the function is an arbitrary function. So I guess, what is the general steps you take to find the normal? I thought it had to do with the...
I am trying to finish the last chapter of Spivak's Calculus on Manifolds book. I am stuck in trying to understand something that seems like it's supposed to be trivial but I can't figure it out.
Suppose M is a manifold and \omega is a p-form on M. If f: W \rightarrow \mathbb{R}^n is a...
Homework Statement
So the test is to take the determinant (D) of the Hessian matrix of your multivar function.
Then if D>0 & fxx>0 it's a min point, if D>0 & fxx<0 it's a max point.
For D<0 it's a saddle point, and D=0 gives no information.
My question is, what happens if fxx=0? Is that...
1. Problem
Define a function:
for t>=0, f(x,t) = { x for 0 <= x <= sqrt(t), -x + 2sqrt(t) for sqrt(t) <= x <= 2sqrt(t), 0 elsewhere}
for t<0 f(x,t) = - f(x,|t|)
Show that f is continuous in R^2. Show that f_t (x, 0) = 0 for all x.
Then define g(t) = integral[f(x,t)dx] from -1 to 1. Show...
Homework Statement
https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xap1/v/t1.0-9/10923273_407123639463753_2874228726948727052_n.jpg?oh=27c882da16071e65bbb420147333ec38&oe=558413E4&__gda__=1434978872_d03c8531060688181560956b68c96650
Is f continuous at (0,0)?
What is the "maximum" region D...
Homework Statement
Evaluate:
I(y)= \int^{\frac{\pi}{2}}_{0} \frac{1}{y+cos(x)} \ dx if y > 1
Homework Equations
The Attempt at a Solution
I've never seen an integral like this before. I can see it has the form:
\int^{a}_{b} f(x,y) dx
I clearly can't treat it as one half of an exact...