Calculus PLEASE check my work ,
posted by anon .
1.) which of the following represents dy/dx when y=e^2x Sec(3x)?
A.3e^2x sec(3x) tan (3x)2e^2x Sec(3x)<<<< my choice
B.)3e^2x sec(3x)tan (3x)2xe^2x sec(3x)
C.)3e^2x sec(3x)tan (x)2e^2x Sec(3x)
D.)3e^2x sec(3x)tan (x)2xe^2x sec(3x)
2.)calculate dy/dx if y=Ln(2x^3+3x)
A.)1/2x^3+3x
B.)1/6x^2+3
C.)2x^3+3x/6x^2+3
D.)6x^2+3/2x^3+3x <<<< my choice
3.)Given the curve that is described by the equation r=3 cos theta, find the angle that tangent lines makes with the radius vector when theta=120.
A.) 30deg
B.) 45deg
C.) 60deg
D.) 90deg << my choice
4.)A line rotates in a horizontal plane according to the equation theta=2^t6t,where theta is the angular position of the rotating line, in radians ,and tis the time,in seconds. Determine the angular acceleration when t=2sec.
A.) 6 radians per sec^2
B.) 12 radians per sec^2
C.) 18 radians per sec^2
D.) 24 radians per sec^2 << my choice.

1. Correct
2. Correct
3.
dy/dx
=(dy/dt) / (dx/dt)
put
x=rcos(t)=3cos²(t)=
y=rsin(t)=3sin(t)cos(t)
Calculate dy/dx and evaluate at t=120° (2π/3) to get
dy/dx=1/√3
=> θ=150°
Angle with radius vector=150°120°=30°.
4.
There may have been a typo in the question. If the question is asking for θ=2^t6t, the answers should not be in round numbers. 
A
line
rotates
in
a horizontal
plane
according
to
the
equation
9
=
2t3
6t,
where
(J
is
the
angular
position
of
the
rotating
line,
in
radians,
and
t
is the
time,
in
sec
onds.
Determine
the
angular
acceleration
when
t
=
2
sec.
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