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A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = -t^3 + 6t^2 + 63t. Determine all intervals when the acceleration of the particle is negative.
A particle moves along the x-axis so that at time t ≥ 0 its position is given by v(t) = 6t^2 - 84t -90. Determine all intervals when the acceleration of the particle is negative.
A particle moves along the x-axis so that at time t≥0 its position is given by x(t) = -t^3 + 14t^2 25t. Determine the velocity of the particle at t = 2.
A particle moves along the x-axis so that at time t≥0 its position is given by x(t) = -t^2 - 13t + 5. Determine the acceleration of the particle at t = 5.
prove that f(x)=[x] is continous everywhere
consider the function f(x)=xcos(x). prove that there exists 0<x<x/2 such that f(x)=x*2/8
Check the validity of Rolle’s Theorem for "f(x)=1+(x-2)^(1\/3)" on the interval [2, 10].
Let {an}∞ n=1 be a convergent sequence with limit L such that B≤an forevery n≥N for some N∈ N and some B∈R. Prove that B≤L
A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = -t^2 - 13t + 5. Determine the acceleration of the particle a t = 5.
Consider the infinite series defined by "\u221e\ufeff\u2211n=1 ((2n!)\/(2^2n))".
(a) What is the value of r from the ratio test?
(b) What does this r value tell you about the series?
