A) Given the following functions, determine whether each of them is a conditional, definitional o...
(a) Determine whether each of the following functions is uniformly continu- ous on the given domain. Justify your answer in each case. (i) f(x) = log (2 + cos(e«)) on R. (ii) g(x) = Väsin ( sin on (0,1).
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks] b) An electronic system contains in components which are connected in series and they i) Describe the meaning of each term in the equation ii) Write down an expression for the unconditional probability P() in terms of iii) Describe the implications omrix)>MYIX). quantities in the above equation. function independently of each other. The length of time for each component until failure follows an exponential...
PHYS10471 2. The following equation occurs in conditional probability: a) 5 marks] B marks 2 marks] b) An electronic system contains in components which are connected in series and they i) Describe the meaning of each term in the equation ii) Write down an expression for the unconditional probability P() in terms of iii) Describe the implications omrix)>MYIX). quantities in the above equation. function independently of each other. The length of time for each component until failure follows an exponential...
2. Sketch the graph of each of the following functions, and determine whether the given function is one-to-one. Show your work! (a) f(x) = -|x +31 – 2 (b) g(x) X + 3 X + 2
1) A perfectly competitive firm faces the following Total revenue, Total cost and Marginal cost functions: TR = 10Q TC = 2 + 2Q + Q2 MC = 2 + 2Q At the level of output maximizing profit , the above firm's level of economic profit is A) $0 B) $4 C) $6 D) $8 *Additional information after I did the math: The price this firm charges for its product is $10, the level of output maximizing profit is 4...
State for each of the following production functions whether it has increasing, or decreasing, or constant returns to scale (pick one for each). Show how you got your answer for each one of them. (i) Q = 3K3/5L2/5 (ii) Q = 12K2+5L2 (iii)Q = 8K+5L (iv) Q = 0.7(K0.4L0.9) (v) Q = min{4K,9L}
1. Decide whether each of the following is an inner product space. Justify your answers. (i) V = Mnxn(R) with (A, B) = tr(AB). (ii) V = M2x2(C) with (A, B) = tr (iii) V = P(R) with (f,g) = f(1)g(1). (iv) V = P(R) with :((1 ;-) B-4). (v) V is the collection of continuous functions from (0, 1) to C, and (5.9) = 'rg() dt. 4.s)-(sat).
Problem 3 (a) Use the definitional method to find the smallest big-O estimate for the following following function. You must determine the multiplicative constant C and the threshold constant k the multiplicative constant C and ihet Show calculation. (b) Use the limit method to formally determine the asymptotic relationship between the following two functions. Show the steps of your calculation and clearly state each rule that you used in the calculation. fn) 100log2n and g(n)-log1on [4+ 4 points] Problem 3...
3. For each of the following functions, (i) Determine the domain, (ii) Find their first derivatives, (iii) Find their second derivatives, (iv) Determine whether they are globally concave? Why or why not? (a) f(x) = 4x? - (b) f(x) = ln(22 - 2) (c) f(x) = e
4. Determine the average function and the marginal function for each of the following functions Totals: a) Total income TR = 100 Q - Q2 b) Total cost TC = 1000+ 10 Q + .01 Q2 c) Total profit TP = 50 Q - 0.1 Q2 - 1000 5. Given the following total income function TR = 100 Q - Q2, determine the level of production that allow to maximize total income. 6. Given the total cost function TC =...