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# Definition of a Limit and Slope of Tangent Line, Midpoint Rule and Trapezoidal Rule, Average and Instantaneous Rate of Change on an Interval

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Use the limit definition to find the slope of the tangent line, f(x)= X^2+2X+1

Use the midpoint rule to approximate the area of the function f(x)=-2x+3 from [0,1]
when n=4. Compare this approximation to the actual area by integration to the approximate area using the trapezoid rule.

Sketch the and find its average rate of change on the interval. Compare this rate with the instantaneous rate of change and the endpoints of the interval f(t)=2t + 7 [1,2]

##### Solution Summary

Definition of a Limit and Tangent Line, Midpoint Rule and Trapezoidal Rule, Average and Instantaneous Rate of Change on an Interval are investigated. The solution is detailed and well presented.

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