Math Answers

Solve the given question shortly
Q. Show that another metric D on a set S is defined by d(x,y)=∫_a^b▒〖|x(t)-y(t)|dt〗

Q. If A is a subspace of l^∞ consisting of all sequence of 0 and 1. What is the induced metric on A? (solve it shortly)

Q. Find all metric on a set X consisting of two points. (solve it shortly)

Q. Compute ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt

Q. solve ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt

Find the basis of M2={(a,b,c,d):a,b,c,d ∈ R}

Let D be a metric on X determined all constant k s.t
(k+d) is a metric. Give its Hint or prove it shortly.

Prove shortly that |d(x,z)-d(y,z)|≤d(x,y) Give its Hint or prove it shortly.

on my video I got 1 right out of 9 how can I fix it?

Let S be the set of all real numbers. Define f: S ~
9.
S by f(s) = S2, and
g: S ~ S by g(s) = s + 1.
(a) Find fog.
(b) Find g 0 f.
(c) Isfog = gof?