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IM3H Module 8 ReviewName:___________________________Limits and Derivatives1. Find the values of the limits using the graph at the right.limx?2f(x)=limx?2+fx=limx?-3f(x)=limx?-5fx=2. Describe the continuity of the graph at the following x-values.If discontinuous, describe the condition of continuity that does not apply and if the discontinuity is removable or non-removable. At x=3, At x=0, At x=-2, 3. Find the values of the following limits algebraically.limx→73x3-147x7-x4. Use the function fx=2x2-2|x-4| x≤-2 -2<x<3x≥3 to find the values of the following limits:limx?-2-f(x)=limx?-2f(x)=limx?3+f(x)=limx?3f(x)=5. Write the equation of the piece-wise function below. Then find the following limits.gx= limx?1-g(x)=limx?1+g(x)=limx?1g(x)=6. Find the derivative of each function. That is, find: f'x=limh→0 fx+h-f(x)h (This equation will NOT be given on test.)fx=-32x-1 kx=x-57.Calculate the average rate of change between x=5 & x=8 on the function, fx=-16x2-112x+1920.8. Calculate the instantaneous rate of change at x=2 on the function gx=-x2+3.502920013335009. Given the graphs below, write the summation notation for the Riemann Sum shown. 25336592075f(x)=(x-6)2+6f(x)=(x-6)2+6Area= Area= 10. Sketch the derivative given function.-1577113900-1577-8320011. Given the equation for gx=3x2-9x+2, find the equation of the tangent line at x=912. At what x-values, does the function fx=2x have a slope of -1/3. 13. Consider the function, gx=-12x2+5 for 0≤x≤3. Estimate 03g(x)dx using right-endpoint rectangles of width 0.75 unit. Follow the steps below as necessary to complete the problem:Sketch a graph showing the curve over the indicated domain. Draw in right-endpoint rectangles from the x-axis to the curve showing a width of 0.75 unit for each rectangle. The rectangles should be below the curve.e. What could you do to make the estimate of 04g(x)dx more accurate?b.Find the height of each rectangle by using the y-values of g(x).c.Write an expression for the sum of the areas of the rectangles.d.Estimate 04g(x)dx.14. Sketch the graph of f(x) given the following features.f'x is positive for all values of x on (-3, 2)f'x is negative if x<-3 or x>2.f1=5f(x)=0 only at x=8f’(x)=0 when x=-6, 3, 5,f(x)>0 for all real numbersf'x>0 on two different intervalsf(0)=4 ................
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