W = o (Co, 1]) and V = c([0,1] IR]

Question

W = o (Co, 1]) and V = c([0,1] IR]

Answer 1

W set of all diff. fun" on [0,1] =

V set of all continuous funn on [0,1] =

The zero vector of v is

an net + € [0,1] zero funnō (a) = 0

We know that,

Every constant fun" is differentiable

ōE W

W 0

Let XER

f and are diff.

We know that

f, gew

d (f+9) df = + dg

da

⇒ f+g is diff

C holds

Also d (xf) = xdf

dal

E W A f W

af is diff

α E W + α E IR fE W

is subspace of V.