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1.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even. 2.Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2. 3.let r>0 and S={x in R^3:(x1)^2+(x2)^2+(x3)^2<(r)^2} show that diam S=2r.4.let x=(x1,...xn) in Rn.show that (? k=1,n xk)^2<=n|x|^2.
Find out the roots of the subsequent pure quadratic equation: Find out the roots of the subsequent pure quadratic equation. 4x 2 - 100 = 0 Solution: Using Equation
Particular to General : When I say 'tail', what do you think of? Do you think of the tail of a horse, or of a monkey? Or do you think of the tail of your pet dog? The tail of
Determine the mean of the subsequent numbers: Example: Determine the mean of the subsequent numbers: 5, 7, 1, 3, 4 Solution: where x' =
Find the discount factors -Linear interpolation: All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765
Harmonic mean It is a measure of central tendency which is utilized to determine the average increase rates for natural economies. This is defined like the reciprocal of the a
If secA= x+1/4x, prove that secA+tanA=2x or 1/2x. Ans: Sec? = x + 1/4x ⇒ Sec 2 ? =( x + 1/4x) 2 (Sec 2 ?= 1 + Tan 2 ?) Tan 2 ? = ( x +
Show the result of the following sequence of UNION operations using union-by-weight with the following assumptions Unions are performed on the representatives on the sets th
To find the distance to nearby stars, the method of parallax is used. The idea is to find a triangle with the star at one vertex and with a base as large as possible. To do this, t
Assume that i) Determine all the roots of f(x) = 0. ii) Determine the value of k that makes h continuous at x = 3. iii) Using the value of k found in (ii), sh
term paper for solid mensuration
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