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Name _____________ Period ____ Honors Brief Calc. Semester 2 Final Exam Review #1 1. lim f ( x) x2 2. For all values of x, f ' ( x) 0 and f ' ' ( x) 0 , draw a curve that could represent a part of the graph of f. 3. Find the slope of the tangent line f ( x) x 2 x when x = 3 4. Find the area enclosed by f ( x) x 2 and g ( x) x 5. The relationship between profit P of a firm and the selling price x of its goods is P 500 x 10 x 2 . What selling price is required to generate a maximum profit? 6. Find the local maximum of y x 4 4x 3 7. If f ' ( x) x 6 x , find f (x) 4 8. Evaluate 1 2 x dx 1 9. Integrate by parts xe dx x 10. If y 4 x 2 2 x 5 then dy at x = 2 is dx 11. If f ( x) (4 x 3) 5 then find f ' ' ( x) 12. Evaluate (4 x 3 6 x 2)dx 13. Write (but do not solve) the integral that expresses the area of the region bounded by the graphs of x 0 , x 4 , and y x 2 14. Find the value of lim x 1 15. Find x2 x 2 x2 1 d x3 3 e dx 16. Solve the differential equation dy x 2 x using the boundary condtion y = 5 and x = 3. dx c 17. For n 1, x n dx equals a 18. For which value does the limit not exist? 19. Use implicit differentiation to find dy if xy 5 x 7 dx 20. Find the limit: lim x 1 x2 1 x 1 21. Let C(x) be the cost function in dollars of producing x units. Let R(x) be the revenue function for selling x units. Write the equation that would be needed to determine how many units should be sold to maximize profit? 22. Evaluate x 2 x 3 5dx ( x h) 2 x 2 23. Find lim at the point x = 3 h 0 h 24. If y cos( x 3 ) , find y ' 25. If f ( x) x2 2 , find f ' ( x) x3