(1)
\int_0^((1)/(2)ln(5)) e^(x)=
(A)
\sqrt(3)
B)
\sqrt(3)-1
C)
\sqrt(5)
(2) The graph of the function
f(x)=(lnx)/(x)
has a relative maximum at
x=
(A)
e
D)
\sqrt(5)-1
(3) From the accompanying figure, the graph of
y=f(x)
is increasing on: A)
(-\infty ,+\infty )
B)
(-\infty ,0]
C)
[0,+\infty )
D)
-1,1
(4) If
f(x)=x^(5)+x^(3)+x
, then
(f^(-1))^(')(0)=
A)
(1)/(3)
B) 3 C) 1 D)
(1)/(9)
(5)
(d)/(dx)[tan^(-1)(x^(3))]=
A)
(3x^(2))/(1+x^(6))
B)
(2x)/(1+x^(4))
C)
(x^(2))/(1+x^(6))
D)
(x)/(1+x^(4))
(6)
sin[2cos^(-1)((3)/(5))]=
A)
(\sqrt(3))/(2)
B)
(24)/(25)
C)
(\sqrt(3))/(4)
D)
(24)/(5)
(7) The domain of the function
y=ln(x^(2)-4x+4)
is: A)
(-\infty ,-2)\cup (2,+\infty )
B)
(-2,2)
C)
(-\infty ,2)\cup (2,+\infty )
D)
(2,+\infty )
(8) The value of
x
such that
3^(x)=2^(x+1)
is: A)
(ln(2))/(ln(3)-ln(2))
B)
ln((2)/(3))
C)
ln((3)/(2))
D)
ln(3)-ln(2)
(9)
\lim_(x->+\infty )(1+(9)/(x))^(5x)=
: A) 1 B) 0 C)
e^(45)
D)
e^((5)/(9))
(10) Let
F(x)=\int_0^x (sint)/(t^(2)+1)dt
. Find
F^(')(0)
; A)
\pi
B) 0 C)
(1)/(2)
D) 1