Across
- 5. method using step size delta x
- 8. theorem that states that if f is continuous on [a,b] then f must take on every y-value between f(a) and f(b)
- 10. the sum of a sequence of numbers
- 12. integral of velocity
- 15. equation involving derivatives and their functions
- 16. infinite series whose terms alternate between negative and positive
- 20. cos(0) approximated using the first three terms of the maclaurin series
- 21. volume of y=6x+2 rotated around the x-axis from x=0 to x=1 (rounded to nearest whole number)
- 22. maclaurin series starting with x-(x^3/3!)+(x^5/5!)-(x^7/7!)
- 23. integral of velocity function
- 25. (e^1)cos(1) approximated using the first three terms of the maclaurin series (truncate to one decimal place)
- 29. area between y=x^2 and y=3x
- 31. when a series has a limit which is finite
- 32. point where f’(x)=0 or f’(x) does not exist
- 33. theorem that states that if f is continuous on [a,b] and differentiable on (a,b) then there exists c in (a,b) such that f’(c)=[f(b)-f(a)]/[b-a]
- 35. a line that touches a curve at a single point (locally)
- 38. derivative of velocity function
- 39. d/dx[f(g(x))]=f’(g(x))g’(x)
Down
- 1. total distance traveled from 1 to 2 of y=t^3 x=cos(t) (truncate to one decimal place)
- 2. approximation of the definite integral using rectangles or trapezoids
- 3. integration method involving fractions
- 4. concavity when velocity is decreasing
- 6. rule used when 0/0 or inf/inf
- 7. graph representing the solutions to a differential equation
- 9. speed when velocity and acceleration have different signs
- 11. concavity when acceleration is positive
- 13. e^3 approximated using the first three terms of the maclaurin series
- 14. L is the ________ capacity
- 17. reverse chain rule
- 18. d/dx[csc(sec(x))]-0.774 x=π/4
- 19. point where concavity changes
- 24. |v(t)|
- 25. ∫(1/(1+x^2))dx b=2π a=0 (round to nearest whole number)
- 26. a function with a break, jump, or hole
- 27. taylor series centered at c=0
- 28. a line that touches a curve at two or more points (globally)
- 30. d/dx[tan(x^2)] x=π/2 (rounded to the nearest whole number)
- 34. when velocity is positive
- 36. ________ error bounds
- 37. test that can be used when f(x) is continuous, positive, and decreasing