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For the following exercises, find the antiderivative of each function
For the following exercises, evaluate the integral.
For the following exercises, solve the initial value problem.
For the following exercises, find two possible functions given the second- or third-order derivatives.
A car is being driven at a rate of mph when the brakes are applied. The car decelerates at a constant rate of ft/sec 2 . How long before the car stops?
sec
In the preceding problem, calculate how far the car travels in the time it takes to stop.
You are merging onto the freeway, accelerating at a constant rate of ft/sec 2 . How long does it take you to reach merging speed at mph?
sec
Based on the previous problem, how far does the car travel to reach merging speed?
A car company wants to ensure its newest model can stop in sec when traveling at mph. If we assume constant deceleration, find the value of deceleration that accomplishes this.
ft/sec 2
A car company wants to ensure its newest model can stop in less than ft when traveling at mph. If we assume constant deceleration, find the value of deceleration that accomplishes this.
For the following exercises, find the antiderivative of the function, assuming
For the following exercises, determine whether the statement is true or false. Either prove it is true or find a counterexample if it is false.
If is the antiderivative of then is the antiderivative of
True
If is the antiderivative of then is the antiderivative of
If is the antiderivative of then is the antiderivative of
False
If is the antiderivative of then is the antiderivative of
True or False ? Justify your answer with a proof or a counterexample. Assume that is continuous and differentiable unless stated otherwise.
If and then there exists at least one point such that
True, by Mean Value Theorem
If there is a maximum or minimum at
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