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If [x] is the greatest integer not greater than x, then determine the limit of [x ]when x goes to (1/2) is it exists
Find limit superior and limit inferior for the sequence (an)n∈N=((1/n)+(-1)^n)n∈N
Go from 0 to 1 on the x-axis, then back half-way to 1/2, then forward half as far to 3/4, then back as half as far to 5/8, then forward half as far, and so on. Give an explicit formula for your position after the nth step. Where do you end up?
Give an upper bound and a lower bound for the expression 1/(a^(4)+3a^(2)+1) if a∈R
Let (X d) be metric space and X is unbounded then d_(1) defined as d_(1)=(d(x y))/(1+d(x y)) x y in X is
a)metric and unbounded
b)metric but may be bounded or unbounded c)metric and bounded
Show that x inverse is not equal to 0 and is unique
Prove A∩(B∩C)=(A∩B)∩C
(a) Justify that In is welled defined and determine its sign.
(b) Show that In is a decreasing sequence.
A mapping f is defined in R^(2*2) , the set of all square matrices of order 2 with entries in R by f: R^(2*2) → R^2
A → Av where v = (-1 2).
(a) Show that f is a linear mapping.
(i)Deduce that for all n E N, we have ㅣUn - sㅣ<= (1/4)^n+1.
Hence, study the convergence of the sequence (Un) and precise its limits.
#339914 on Dec 2023