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    Maximisation problem / costs: Consider a firm with two inputs K and L...

    Consider a firm with two inputs K and L that produce an output Q(K, L). The firm’s cost function is C(K, L) = K + 2L It is required to minimize C(K, L) subject to the constraint Q(K, L) = q where q is a positive real constant. You may assume that the optimization problem has a solution at an...
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    deriving finite difference scheme for partial differential equation.

    Hi, Can anyone help with the last part of this question, I just cannot seem to derive the scheme! \frac{u_{j}^{n+1}- u_{j}^{n-1}}{ 2 \Delta t} - 5 \frac{u_{j+1}^{n} - u_{j-1}^{n}}{ 2 \Delta x } = 0
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    row reducing matrix,

    You see in my example, the next pivot is at -2, i.e along the diagonal. However the qustion says if we were to choose the next pivot entry above it, i.e -3 what would happen?
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    row reducing matrix,

    I think that one is already row reduced? I dont think I am misunderstanding the directions?
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    row reducing matrix,

    When looking for a possible new pivot, why do we only search from row k to n in column k? In other words, what unwanted thing could happen if we used a row above row k as the new pivot row? am not really sure why, we choose the next pivot to be below the kth...
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    help numerical analysis

    For any integer value of n, define F(n) as the combined operation count of forward and backsubstitutions and define G(n) as the operation count of gaussian elimination. When n gets larger and larger,why does F(n) grow much more slowly that G(n) does? I have no idea why? can anyone point me in...
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    angular velocity

    if your solving for v, than isnt the answer \sqrt{ga} = v ? my book says the correct answer is \dot{\phi} > \sqrt{\frac{g}{a}} I dont understand how they got this? can anyone explain? ( I know we are using newtons second law in polar coordinates ) thanks
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    angular velocity

    I understand the situation, but dont quire understand how to put this into formula. how do
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    angular velocity

    1)A light bucket contains a ball of mass m. The bucket is attached to a rigid rod and swung in a vertical circle at a constant angular velocity. The distance from the pivot point to the bottom of the bucket is a. What is the minimum angular velocity of the bucket such that the ball does not...
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    calculation torque help!

    Hello, Can someone please just clarify my notes for me, i really cant understand how my teacher gets j = - cos \phi \hat{\phi}-sin \phi \hat{r} I have attached the question and solution, but i have no idea how to work out j, the unit vector in terms of phi and r, please can someone show...
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    proof by induction help

    Am afraid i dont follow, here is the solution and i cant understand it from the second line onwards.
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    proof by induction help

    Let *^{n}(a) = {a*.......*a } n times thus *^{1} = a *^{2} = a*a *^{3} = a*a*a etc prove by induction that *^{n}a = (a+1)^{n} -1 for all n in N am really having problems understand how to do this, please can someone show a step by step solution guide? so far i...
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    sequence divergence proof

    oh goodness, now i get it! I just get very confused with rules of inequalities, its so confusing. But thank you , it all makes sense now.
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    sequence divergence proof

    understand where 2 'came from' but not where the sin (n) function 'went to', could you explain that bit ? thanks
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    sequence divergence proof

    well sin is bounded between -1 and 1,
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    sequence divergence proof

    thank you, but I still dont understand what happened to sin (n) ? you go from \sqrt{n} -2sin(n) to \sqrt{n} -2 how?
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    sequence divergence proof

    a_{n} = \sqrt{n} + 2sin (n) let m >0 take N= (2+m)^{2} and let n >N then \geq \sqrt{n} -2 > 2+m-2 = m because n >N \sqrt{n} > \sqrt{N} = 2+m where does N come from ? we want a_{n} > m start with a_{n} = \sqrt{n} + 2sin (n) > \sqrt{n} -2 which exceeds m...
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    convergence / divergence help

    could you explain how you got this ? Is there a general rule to show that a sequence converges/ diverges ? thank you
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    convergence / divergence help

    a_{n} = \dfrac{n^{3}}{1+ln(n)} a) for all n ∈ N. Say whether this sequence is divergent, convergent, and/or bounded. i think this sequence is divergent, just from looking at it? b) Give a proof of your answer to part (b). Standard properties...
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    sequence divergence proof

    I understood it now, thank you.
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