Calculus Writing Assignments

You are going to answer 3 differents question

1/ One difference between algebra and calculus is the ability to calculate instantaneous rate of change. Let R(t) be defined as a function describing numerically the quality of your relationship with God at time t = now. For example, if R(t) is large positive, then you have an extremely good intimate relationship with God. If R(t) is large negative, then it would be describing an extremely bad or antagonistic relationship with Him. The question to answer is: “What would the derivative of R(t) be for you and what is the significance of knowing the instantaneous rate of change as opposed to average rate of change?”
Explain your answer thoroughly and carefully. For example, one possible answer would be “R’(t) would be large positive because at this moment I am drawing closer to Him very rapidly”.

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2/ What is the relationship of the chain rule to implicit differentiation?

3/ Why is important to know the theoretical foundations of the integral (area under a curve), especially for integrands that do not have antiderivatives? Explain. How does this relate to the theoretical foundations of the will of God (being familiar with God and His Word) and understanding the will of God for your own life?

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