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Four relations a to d are defined on sets A and B. Which of the relations represent a function from A to B?.

a. f1 and f2

b.f1 and g1

c. f2 and g1

d. f2 and g2

a. f1 and f2

b.f1 and g1

c. f2 and g1

d. f2 and g2

Let {bn} be a sequence such that bn = 1 + (1/n). Prove that inf(bn) = 1

using delta - epsilon definition prove that lim(x-->0) (sinx/x) = 1

solve the given question shortly

Q. Find all metric on a set X consisting of two points.

Q. Find all metric on a set X consisting of two points.

Q. Prove shortly that normed linear space is also a metric space.

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

solve the given question shortly

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

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

Q. Let D be a metric on X determined all constant k.

Prove shortly that k+d is a metric.

Prove shortly that k+d is a metric.

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

Q.Let D be a metric on X determined all constant k s.t

(i) kd is a metric

(ii)(k+d) is a metric

(i) kd is a metric

(ii)(k+d) is a metric