lim(x->; ∞)( 1 + 1/x)^ 10 = 1
lim(x->; ∞)( 1 + 1/ 10)^x->; +∞
A: A.
(2)
f(x)=∫( 1-& gt; X) SGD/T.
f'(x) = sinx/x
∫(0->; 1) xf(x) dx
=( 1/2)∫(0->; 1)dx^2
=( 1/2)x^2.f(x)]|(0->; 1)-( 1/2)∫(0->; x^2.f'(x) dx
=( 1/2)x^2.f(x)]|(0->; 1)-( 1/2)∫(0->; 1) xsinx dx
=( 1/2)f( 1)+( 1/2)∫(0-& gt; 1) x dcosx
= 0+( 1/2)[xcosx]|(0-& gt; 1)-( 1/2)∫(0->; 1) cosx dx
=( 1/2)cos 1-( 1/2)[sinx]|(0-& gt; 1)
=( 1/2)cos 1-( 1/2)sin 1
A: B.
(3)
f(x) = x^p +( 1-x)^p
=px^(p- 1 -p( 1-x)^(p- 1)
f'(x)=0
px^(p- 1)-p( 1-x)^(p- 1)=0
x= 1-x
x= 1/2
f '(x)| x = 1/2+& lt; 0,f '(x)| x = 1/2-& gt; 0
X= 1/2 (minimum)
Minimum f(x)
=f( 1/2)
= ( 1/2)^p +( 1/2)^p
=( 1/2)^(p- 1)
A: C.