Calculus Answers

Consider a particle moving along the x-axis where x(t) is the position of the

particle at time t, x′(t) is its velocity, and x

′′(t) is its acceleration.

If x(t) = t3

− 6t2 + 9t − 2, 0 ≤ t ≤ 5

(a) Find the velocity and acceleration of the particle. (b) Find the open

t-

intervals on which the particle is moving to the right. (c) Find the velocity of

the particle when the acceleration is 0

Find the angle of the largest right circular cone which can be inscribed in a sphere of

radius 9 inches.

: Let 𝑓(𝑥, 𝑦) = 𝑥^2 + 𝑦^3 . Find the slope of the line tangent to this surface at the point (-1, 1) and lying in the plane x = -1

Solve using basic differentiation rule

y = 2/(x ^ (1/2)) + 6/(x ^ (1/3)) - 2/(x ^ (3/2)) + 4/(x ^ (3/4))

Solve using differentiation rule

y = 2x ^ 2 * sqrt(2 - x)

Solve using basic differentiation rule

𝑠 = (𝑡^2 − 3)^4

Solve using basic differentiation rule

𝑔(𝑥) =3−2𝑥/3+2𝑥

Find the area, take the elements of the area perpendicular to the x-axis. x²-y+1=0; x-y+1=0.