Given the region

E

enclosed by these curves

y=x^(2)-(lnx)/(8),x=1,x=t

and

y=0

, where

t>1

is a real number. Denote

A(t)

as the area of the region

E

, and

L(t)

as the perimeter () of

E

, i.e. the total length of the boundary (outer edge) of

E

.\ (A)

(5pts)

If\

L(t)=at^(2)+bt-1

\ for some real numbers

a

and

b

, then

(a,b)=(1)_()

.\ (B)

(5pts)

If\

A(t)=pt^(3)+q(t-tlnt)+r

\ for some real numbers

p,q

and

r

, then

(p,q,r)=(2)_()

.\ (C)

(5pts)

There exist real numbers

\\\\alpha

and

\\\\beta >0

such that

\\\\lim_(t->\\\\infty )(A(t))/(t^(\\\\alpha )L(t))=\\\\beta

. Then

(\\\\alpha ,\\\\beta )=(3)_()

.

Given the region E enclosed by these curves y=x28lnx,x=1,x=t and y=0, where t>1 is a real number. Denote A(t) as the area of the region E, and L(t) as the perimeter () of E, i.e. the total length of the boundary (outer edge) of E. (A) (5pts) If L(t)=at2+bt1 for some real numbers a and b, then (a,b)=(1). (B) (5pts) If A(t)=pt3+q(ttlnt)+r for some real numbers p,q and r, then (p,q,r)=(2). (C) (5pts) There exist real numbers and >0 such that limttL(t)A(t)=. Then (,)=(3)