Bounded metric
Prove the following Theorem. If (X,d) is a metric space, then there is bounded metric on X which is equivalent to d. recall: When we say a metric p is bounded, we mean that there exists an M >0 such that p(x,y) <= M for all x,y in X.
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Show that the following equation has a solution of the form u(x,y) = e^(ax+by). Find the constants a and b: u_xx + u_yy = 5e^(x-2y)
The following data can be employed to approximate the integral: M = ?3? ÷ 2 0 cos x dx N1(h) = 2.356194 N1(h ÷ 2) = -0.4879837 N1(h ÷ 4) = -0.8815732 N1(h ÷ 8) = -0.9709157 Suppose a formula exists of the type given in
Find out whether the given differential equation is exact. If it is exact, solve it. (y ln y ? e?xy) dx + (1/y + x ln y) dy = 0.
Find the value of k so that the given differential equation is exact. (y^3 + kxy^4 ? 2x) dx + (3xy^2 + 24x^2(y^3)) dy = 0.
Determine the relation between recursion and induction? How do you go about finding an explicit (closed-form) formula for a recursion relation?
Find out the current i at any time t after the switch is closed. 3 Determine the maximum current that can be obtained from the simple circuit?
Suppose that the risk free rate is 3.5%. Determine the premium of one-year call option with strike price of $38.50, if the profit of the buyer of the call is $4.78 and stock spot price is $44.34 at the end of the year.
A DNA chain is string of As, Ts, Gs, and Cs. How many DNA chains are there of length 12 which have the following properties? Has string of 10 or more consecutive Gs.
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