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b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the amount of sand that has exited the container on 1sts9. Show your process. c) Is the amount of sand in the tank increasing or decreasing att = 4. Give a reason for your answer.

b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the amount of sand that has exited the container on 1sts9. Show your process. c) Is the amount of sand in the tank increasing or decreasing att = 4. Give a reason for your answer.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Calculus BC piecewise function

Consider the piecewise defined function w(t) modeling the rate at which sand enters a container, and the differentiable function G(t) modeling the rate at which sand leaves the container. Both functions are measured in L/hr and at t = 1 hour there are 500 L in the container. I> 2 3cos( 51 – 10) + 13, 0<1<2 |1 4 9 12 G), L/hr 10 8 15 22 t 61 + 4, w( t) = a) Is w(t) continuous at t = 2? Is w(t) differentiable at t = 2? Justify your answer. b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the amount of sand that has exited the container on 1sts 9. Show your process. c) Is the amount of sand in the tank increasing or decreasing at t = 4. Give a reason for your answer. d) Using Mean Value Theorem yields the approximation for G'(2.5) . Using correct units, explain the meaning of this value in the context of the question. 3 e) Evaluate Í w(t)dt. Show your process. (remember don't simplify) 1 f) Write an equation that would represent the time K when the container has 545 L of sand in it. Do not solve. g) Consider the function given by h'(t) = w(t) + G(t) and give the second degree Taylor polynomial centered at t = 4 for h(t). It is known that h(4) = 20 and G'(4) = -9. h) Write an expression for the length of w(t) from t = 0 to t = 2. Do not solve. i) Find an antiderivative that could be used to evaluate į t - G"(t)dt. a
Transcribed Image Text:Consider the piecewise defined function w(t) modeling the rate at which sand enters a container, and the differentiable function G(t) modeling the rate at which sand leaves the container. Both functions are measured in L/hr and at t = 1 hour there are 500 L in the container. I> 2 3cos( 51 – 10) + 13, 0<1<2 |1 4 9 12 G), L/hr 10 8 15 22 t 61 + 4, w( t) = a) Is w(t) continuous at t = 2? Is w(t) differentiable at t = 2? Justify your answer. b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the amount of sand that has exited the container on 1sts 9. Show your process. c) Is the amount of sand in the tank increasing or decreasing at t = 4. Give a reason for your answer. d) Using Mean Value Theorem yields the approximation for G'(2.5) . Using correct units, explain the meaning of this value in the context of the question. 3 e) Evaluate Í w(t)dt. Show your process. (remember don't simplify) 1 f) Write an equation that would represent the time K when the container has 545 L of sand in it. Do not solve. g) Consider the function given by h'(t) = w(t) + G(t) and give the second degree Taylor polynomial centered at t = 4 for h(t). It is known that h(4) = 20 and G'(4) = -9. h) Write an expression for the length of w(t) from t = 0 to t = 2. Do not solve. i) Find an antiderivative that could be used to evaluate į t - G"(t)dt. a
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