Answer to Question #63505 in Calculus for hoseph ogala

Question

1 Given that
A=sinti+costj+tk
A=sin⁡ti+cos⁡tj+tk

, evaluate
∣∣∣d2Adt2∣∣∣
2 A particle moves along a curve whose parameter equations are
x=e−t
x=e−t
,
y=2cos3t
y=2cos⁡3t
,
z=2sin3t
z=2sin⁡3t
. Find the magnitude of the acceleration at t=0
3 A particle moves along the curve
x=2t2
x=2t2
,
y=t2−4t
y=t2−4t
and
z=3t−5
z=3t−5
,where t is the time. Find the components of the velocity at t=1 in the direction
i−3j+2k
4 Determine the unit tangent at the point where t=2 on the curve
x=t2+1
x=t2+1
,
y=4t−3
y=4t−3
and
z=2t2−6t
5 If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A⋅B)