Calculus
posted by Someone .
A particle moves along the xaxis with position function s(t) = e^cos(x). How many times in the interval [0, 2π] is the velocity equal to 0?
1< My answer
2
3
More than 3
I don't really get this question will someone please explain it to me?

v(x) = sin(x) e^cos(x)
since e^cos(x) is never zero, how many times in sin(x) = 0 in the interval?
Your answer is correct on the interval (0,2π), but not on [0,2π] 
what is the difference between the two?

v(t) = 0 at 0,π,2π
If you exclude the endpoints of the interval, your answer is correct. But, we are working with the closed interval, including the endpoints. So, there are 3 points where v(t) = 0.
Better review interval notation.
Respond to this Question
Similar Questions

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 … 
calc
i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given … 
Calculus
A particle moves along the xaxis with velocity v(t) = (t3)² + 5 for [0,6]. a) Find the average velocity of this particle during the interval [0,6]. b) Find a time t* ∈ [0,6] such that the velocity at time t* is equal to the … 
Calculus
A particle moves along the xaxis with the velocity given by v(t)=3t/(1+t^2) for t >or equal to 0. When t=0, the particle is at the point (4,0). 1. Determine the maximum velocity for the particle. Justify your answer. 2. Determine … 
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) … 
math
A particle moves along the xaxis with position function s(t) = esin(x). How many times in the interval [0, 2π] is the velocity equal to 0? 
calc
A particle moves along the xaxis with position function s(t) = e^(cos(x)). How many times in the interval [0, 2π] is the velocity equal to 0? 
Calculus
A particle moves along the xaxis and its position for time t is greater than or equal to 0, is s (t)=cos(2t)+sec(t). When t=pi, the acceleration of the particle is 
Calculus
The Question: A particle moves along the Xaxis so that at time t > or equal to 0 its position is given by x(t) = cos(√t). What is the velocity of the particle at the first instance the particle is at the origin?