Calculus Final Project

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Across
  1. 3. Function, f(t) moves in one direction as its argument t increases
  2. 6. the limit from both sides are equal
  3. 7. the expression that represents the addition of infinitely many quantities
  4. 8. the derivative of velocity with respect to time
  5. 9. Rate of Change, slope of a tangent at a point or value of a derivative at a point
  6. 10. theorem, for any function in which f(a)= f(b), there exists a point x where f'(x) = 0. x must be between a and b
  7. 12. function, functions if which -f(x) = f(-x) for all x values
  8. 14. the change in position with respect to time
  9. 19. a quantity that has direction and magnitude
  10. 21. Rule, if f(x) = g(h(x)) then f’(x) = g’(h(x))*h’(x)
  11. 24. of inflection, when the graph changes from concave to convex or the sign of y' changes
  12. 27. Value theorem,if a function takes on the value y1 and y2 at a and b respectively. Tehre must exist a value between a and b for any value between y1 and y2
  13. 28. Lines, lines that intersect a graph at a single point
  14. 30. discontinuity, points at which there are holes. They occur when the value can be found in simplified versions of the function, but not the original.
  15. 31. Series, polynomials with an infinite number of terms
  16. 32. points at which the curve or line intersect the x and y axes
  17. 33. a mathematical technique for finding a maximum or minimum value of a function of several variables subject to a set of constraints
  18. 36. Theorem of Calculus, The integral of the function f(x)dx on the interval a through b is equal to f(b)-f(a)
  19. 38. Extrema, the maxima and minima of some enclosed interval
  20. 39. Term Test, if the series grows without bound series diverges
  21. 40. Rule, (x^n)’ = nx^(n-1)
  22. 41. Minimum, the lowest point over the domain of the function
  23. 42. Value, 1/(b-a) * integral of f(x)dx
  24. 44. Riemann Sum, using the left end points of rectangles to evaluate the area under the curve
  25. 45. Value theorem, if a function is continuous on the interval [a,b], then there must exist both a maximum and a minimum on the interval
  26. 48. Field, graphical representation of the solution to a differential equation
  27. 49. set of numbers that follow some sort of rule
  28. 50. series, taylor series at x=0
Down
  1. 1. functions that can be integrated
  2. 2. form, 0/0 or infinity/infinity
  3. 4. discontinuity, points at which the function does not meet so the limit cannot be evaluated
  4. 5. using tangent lines to estimate values of a function
  5. 11. refers to terms for which the derivative can be taken
  6. 13. Integral, an integral which is bounded by two points generally referred to as "a" and "b"
  7. 15. Point, values where f(x) is equal to 0 or infinity
  8. 16. quantity that influences a behaviour of a mathematical object
  9. 17. Curve, shape constructed using the polar system
  10. 18. Rule, rule that states derivative of a constant function is 0
  11. 20. Theorem, The squeeze theorem states that if f(x)≤g(x)≤h(x) for all numbers and at some point x=k we have f(k)=h(k) then g(k) must also be equal to them
  12. 22. Differentiation, a procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
  13. 23. Rate of Change, slope of a secant line between two very close points in order to estimate the instantaneous rate of change
  14. 25. Asymptotes , x-values at which f(x) is undefined
  15. 26. to One Function, each value in the domain has a unique output
  16. 29. Maximum, the highest point over the domain of the function
  17. 34. rule, (uv)' = uv' + vu'
  18. 35. Fractions, expressing a fraction as the sum of polynomials with simpler denominators
  19. 37. Function, a function that reverses the original function
  20. 38. Rule, used when the limit is indeterminate. Evaluate the derivative of the numerator and denominator separately and attempt to plug in the value
  21. 40. functions, functions that have several parts and have different rules for different portions of the domain
  22. 43. function, functions in which f(x)=f(-x) for all x values
  23. 46. down, occurs when y' is decreasing and y'' is negative
  24. 47. expression that consists of variables and coefficients