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. Bothfunctions are measured in L/hr and at t = 1 hour there are 500 L in the container.I> 23cos( 51 – 10) + 13, 0<1<2|1 4 9 12G), L/hr 10 8 15 22t61 + 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 theamount 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 youranswer.d) Using Mean Value Theorem yields the approximation for G'(2.5) . Using correctunits, explain the meaning of this value in the context of the question.3e) Evaluate Í w(t)dt. Show your process. (remember don't simplify)1f) Write an equation that would represent the time K when the container has 545 L of sand in it. Donot solve.g) Consider the function given by h'(t) = w(t) + G(t) and give the second degree Taylor polynomialcentered 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

Name: Calculus BC piecewise function Consider the piecewise defined function
Uploaded: 2024-03-20T06:38:44.000Z
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Description: 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. Bothfunctions are measured in L/