Calculus Puzzle

This puzzle has simple problems, theorums, and properties that are an integral part (no pun intended) of calculus. A few words on notation. 3x^2 = threexsquared 3 = three 0 = zero sin x = sinx sin 2x = sintwox sin^2 x = sinsquaredx 1/x = oneoverx 1/(x-1) = oneoverxminus1 infinity = infinity NOTE: For all indefinite integrals, forget about the + C. NOTE: For all true/false questions, I changed the wording a bit. I will give you a positive/negative expression: IE: True/False, Yeah/Nope, Yay/Nay, and you have to pick the correct one.

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Across 8. (b-a)/2n[f(x0) + 2f(x1) + 2f(x2)...+ f(xn)] is the general formula for which rule. 9. True/False: the derivative of position is velocity 11. The Integral of a function is equal to its _______ + C. 14. Find dy/dx: y = 3 14. Find dy/dx: y = 900000000000000 14. Find the antiderivative: y = 0 14. find d^2y/dx: y = 3x 18. Aff/Neg: The limit definition to find area using "n" subintervals, as n approaches infinity, is an accurate measure of the area under the curve on a specified interval 19. If the second derivative is zero the seconcd derivative test _____. 20. Yeah/Nope The trapezoidal rule is the exact value for the area under the curve. 21. The antiderivative of cos (3x) is this. 24. Functions that either increase or decrease along its entire domain are called ________. 25. Find the area under the curve y = 3x^2 on the interval [-1,1] 26. A functious is not continous if its left hand limit does not _____ its right hand limit.

Down 1. The derivative represents the average ____ of change. 2. Yeah/Nope: not every function has an inverse. 3. Find dy/dx: ln x 4. You are given dy/dx: What test do you use to find increasing and decreasing intervals of f(x)? 5. Find dy/dx: y= 4x^3 6. If the second derivative is positive along that interval, the graph of the function is always this. 7. Yay/Nay: The mean value theorum states that only monotonic functions have an inverse. 10. The area under the curve for f(x) is found by using this process. 11. The second derivative of position is this. 12. The slope of the tangent line is also known as this. 13. Yes/No: the derivative of the integral of f(x) is simply f(x). 15. True/False: Rolles theorum states that the integral of f(x) is equal to the area of f(x) along a specified interval. 16. When the first derivative is negative at the left of the critical point and positive at the right of the critical point, the critical point is a relative ___________. 17. The horizontal asymptote of f(x) is the limit as x approaches what value? 22. Aff/Neg: Reimann sums measure the slope of the tangent line 23. Find the antiderivative: y = 1

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