COntinuaus functions Uni fo and thot canvege pointluibe in Doe K Exists COntinuaus functions Uni fo and thot canvege pointluibe in Doe K Exists
You have 4.7 moles of a gas that undergoes a Carnot Cycle where THot=305 K, and TCold=239 K and the chamber fluctuates between 7.9 L and 17.5 L. Determine the work that is performed by the gas and the heat transferred for one cycle. Express your answer in Joules to the first decimal place (XXXX.X).
Let {yk}k=1infinity be a sequence of differentiable functions which map [a,b] to Rn. Assume the sequence {yk(a)}k=1infinity is bounded. Assume the sequence of derivatives {yk' }k=1infinity is uniformly bounded: there exists a number M such that ||yk'(t)|| <= M for all t E [a,b] and k = 1,2,3.... Prove that there exists a sub-seqeunce {kj}j=1infinity such that the sequence {ykj}j=1infinity is convergent uniformly in [a,b].
Integral Transform
Find the Fourier Sine transform of the following functions: (a) F {e-a2} (b) Fo{qz1a2}
Let G be a bipartite graph of maximum degree k. Show that there exists a k – regular bipartite graph, H, that contains G as an induced subgraph.
Exercise 3. [10 pts Let n 2 1 be an integer. Prove that there exists an integer k 2 1 and a sequence of positive integers al , a2, . . . , ak such that ai+1 2 + ai for all i-1, 2, . . . , k-1 and The numbers Fo 0, F1 1, F2 1, F3 2 etc. are the Fibonacci numbers
4. (10 points) Prove that the following statement is false. There exists an integer k > 4 such that k is a perfect square and k – 1 is prime.
Solve for infiltration constant K when fo = 5mm/hr, fc = 0.9 mm/hr and f = 3.6 mm/hr at hour 2.
It is known that mgf of random variable X exists. Kth moment m is as below, what is mgf of X? К! k 0,1, . Eosisk/2 (k-21) (а) тк (r+k-1)!k k 0,1, . (r = positive integer) (b) тк — (r-1)!
It is known that mgf of random variable X exists. Kth moment m is as below, what is mgf of X? К! k 0,1, . Eosisk/2 (k-21) (а) тк (r+k-1)!k k 0,1, . (r = positive integer) (b) тк...
1/2 b dr Problem 1: Suppose that [a, b] exists R, and let V be the space of all functions for which and is finite. For two functions f and g in V and a scalar A e R, define addition and scalar multiplication the usual way: (Af)(x) f(x) f(x)g(r) and (fg)(x) Verify that the set V equipped with the above operations is a vector space. This space is called L2[a, b
1/2 b dr Problem 1: Suppose that [a,...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...