Calculus  Still Need Help! Anyone!
posted by Leanna .
A particle moves along the xaxis with position at time t given by x(t)=e^(t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi.
a) Find the time t at which the particle is farthest to the left. Justify your answer
I think you have to find the prime of this equation and then see when it is negative.
b) Find the value of the constant A for which x(t) satisfies the equation Ax"(t)+x'(t)+x(t)=0 for 0 is less than t which is less than 2 pi.
I have no idea how to even start this problem.

a. Find the derivative, set to zero
dx/dt= e^t * sint+ e^tcost=0
tanT=1 check that.
t= PI/4 or 3PI/4
Now which will make it to the left (negative x)?
b. d^2x/dt^2= d/dx e^t(costsint)
take that dervative.
Then, put in the equation given
ax" + x'+ x=0 and solve for A
Respond to this Question
Similar Questions

Calculus (Answer Check)
Are my answers right? If they are wrong you don't have to tell me how to do it its okay =) A particle starts at time t=0 and moves along the xaxis so that its position at any time t(greater or equal to) 0 is given by x(t)=(t1)^3 
Calculus (Answer Check)
A particle moves along the xaxis so that its velocity at time t, 0(less than or equal)t(greater or equal to)5 is given by v(t)=3(t1)(t3). at time t=2 the position of the particle is x(2)=0. 1. find the minimum acceleration of the … 
Calculus (Answer Check)
A particle moves along the xaxis so that its velocity at time t, 0(less than or equal)t(greater or equal to)5 is given by v(t)=3(t1)(t3). at time t=2 the position of the particle is x(2)=0. 1. find the minimum acceleration of the … 
Calculus
A particle moves along the xaxis with position at time t given by x(t)=e^(t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your … 
Calculus
A particle moves along the xaxis with position at time t given by x(t)=e^(t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your … 
Calculus!!!!
A particle moves along the xaxis with position at time t given by x(t)=e^(t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your … 
calculus
a particle moves along the y axis so that its position at any time t, for 0 is less than or equal to t which is less than or equal to 5, is given by y(t)=t^418t^2. in which intervals is the particle speeding up? 
Calculus
Two particles move along the x axis. For 0 is less than or equal to t is less than or equal to 6, the position of particle P at time t is given by p(t)=2cos((pi/4)t), while the position of particle R at time t is given by r(t)=t^3 … 
Calculus
Two particles move along the x axis. For 0 is less than or equal to t is less than or equal to 6, the position of particle P at time t is given by p(t)=2cos((pi/4)t), while the position of particle R at time t is given by r(t)=t^3 … 
Calculus
Hi! I need help with this problem: For 0(smaller or equal to) t (smaller or equal to) 9, a particle moves along the xaxis. The velocity of the particle is given by v(t)= (sin pi/4 t). The particle is at position x= 4 when t=0. a) …