Average Rate of Change Over an Interval - Page 12

Questions
  • Water is building up in a bathtub. After 2 minutes there are 12 gallons of water and after 4 minutes, there are 20 gallons of water. What is the average rate at which water is entering the bathtub from #t=2# to #t=4# minutes?
  • Average of sin t *cos t how to find ?
  • A broken pipe leaks #5 1/2# gallon of water every #1/4# hour. To the nearest hundredth, determine the rate at which the broken pipe leaks water in gallons per minute?
  • The hands on a clock are of length 15mm (minute hand) and 12mm (hour hand). How fast is the distance between the tips of the hands changing at 3:00?
  • A square plate of metal is expanding under the action of heat, and its side is increasing at the uniform rate of 0.1 cm per hour. What is the rate of increase of its area at the moment when the side is 16cm long?
  • What is the average rate of change for the function over the interval, #f(x)= 3/(x-2)# between #x =4# and #x=7#?
  • A spherical balloon is being inflated so that its volume is increasing at the rate of 10cm3/sec. Find the rate at which the diameter is increasing when the diameter is 20cm?
  • Let y = 10x^3+2x^2+5 a. find the average of change at which y changes with x over the interval [2,5]? b. find the instantaneous rate of change y with respect to x at the point x = -1?
  • What is the average value of the function #f(x) = 3/x# on the interval #[1,2e]#?
  • What is the average value of the function # f(x) = sin^2 (x) # on the interval #[0, pi]#?
  • Water is building up in a bathtub. After 2 minutes there are 12 gallons of water and after 4 minutes, there are 20 gallons of water. What is the average rate at which water is entering the bathtub from #t = 2# to #t = 4# minutes?
  • What is the average rate of change of the function #y=3^x# over the interval #[0,1]#?
  • For #f(x) = .01(2)^x#, how do you find the average rate of change from #x=12# to #x=15#?
  • How can you define different continuous functions #f(x)# and #g(x)# with #f(0) = g(0)# and the same average rate of change over the interval #[0, 2]# ?