Questions in Section Calculus I: page 8

A storage tank in the shape of a right circular cone has a height of 10 feet. The top rim of the tank is a circle with radius 4 feet. If liquid is being pumped into the tank at the rate of 2 cubic feet per minute, what is the rate of change of the depth of the liquid (in feet per minute) when the depth is 5 feet?

A rocket is modeled by a particle that moves along a vertical line. From launch, the rocket rises until its motor cuts out after 17 seconds. At this time it has reached a height of 580 meters above the launch pad and attained an upward velocity of 120 `m/s`. From this time on, the rocket has constant upward acceleration −10 `m/s^2` (due to the effect of gravity alone).Choose the s-axis (for the position of the particle that represents the rocket) to point upwards, with origin at the launch pad. Take `t = 0` to be the time when the rocket motor cuts out.

Let `f(x)=x/(|__x__|)` where `|__x__|` is the floor function. It takes any value of `x` and rounds it down to the nearest integer. Evaluate:

  1. `lim_(x->2^-)f(x)`
  2. `lim_(x->2^+)f(x) `
  3. `lim_(x->2)f(x) `

Consider the functions `f(x)=(x^2-1)/(x^2-3x+2)` and `g(x)=tan(3x)/(4x^2-7x)`.

  1. if the limit exists, evaluate `lim_(x->1)f(x)`.
  2. if the limit exists, evaluate `lim_(x->2)f(x)`.
  3. if the limit exists, evaluate `lim_(x->0)g(x)`.

Use logarithmic differentiation to find derivative of `y=sqrt(x)e^(x^2-x)(x+1)^(2/3)`.

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