Calculus Puzzle

Calculus Puzzle

Achuta Kadambi

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

3. The slope of the tangent line is also known as this.

6. Find the antiderivative: y = 0

7. Yes/No: the derivative of the integral of f(x) is simply f(x).

9. (b-a)/2n[f(x0) + 2f(x1) + 2f(x2)...+ f(xn)] is the general formula for which rule.

11. Find dy/dx: y= 4x^3

13. The derivative represents the average ____ of change.

14. Functions that either increase or decrease along its entire domain are called ________.

20. The second derivative of position is this.

21. True/False: Rolles theorum states that the integral of f(x) is equal to the area of f(x) along a specified interval.

22. Yeah/Nope The trapezoidal rule is the exact value for the area under the curve.

23. 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

24. If the second derivative is positive along that interval, the graph of the function is always this.

26. Find dy/dx: y = 900000000000000

27. The horizontal asymptote of f(x) is the limit as x approaches what value?

Down

1. You are given dy/dx: What test do you use to find increasing and decreasing intervals of f(x)?

2. Aff/Neg: Reimann sums measure the slope of the tangent line

4. The Integral of a function is equal to its _______ + C.

5. 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 ___________.

8. Find dy/dx: ln x

10. A functious is not continous if its left hand limit does not _____ its right hand limit.

12. Find the antiderivative: y = 1

15. Find the area under the curve y = 3x^2 on the interval [-1,1]

16. Yeah/Nope: not every function has an inverse.

17. Find dy/dx: y = 3

18. The antiderivative of cos (3x) is this.

19. The area under the curve for f(x) is found by using this process.

22. Yay/Nay: The mean value theorum states that only monotonic functions have an inverse.

25. If the second derivative is zero the seconcd derivative test _____.

26. find d^2y/dx: y = 3x

28. True/False: the derivative of position is velocity

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