Calculus

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Across
  1. 4. A function is ___ at a point "a" when f(a) matches the limit of f as x approaches a.
  2. 6. Abbreviation; theorem that states that the antiderivative of a derivative of a function is the function itself
  3. 8. ___ growth is a model for a quantity that increases quickly at first and then more slowly as the quantity approaches an upper limit.
  4. 9. Abbreviation; If f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval.
  5. 12. ___ rule is used to find the derivative of two functions divided by one another, such as (e^x)/(x^2).
  6. 15. The ___ of convergence “R” is any number such that the power series will converge for |x – a| < R and diverge for |x – a| > R.
  7. 17. ___ sum. An approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids.
  8. 20. ___ error bound. Gives the worst-case scenario for the difference between the estimated value of the function as provided by the Taylor polynomial and the actual value of the function.
  9. 23. The ___ line passes through two points of a curve.
  10. 25. Used to calculate the net area under a curve
  11. 26. Abbreviation; If f is continuous on the closed interval [a, b], then f must attain a maximum and a minimum, each at least once.
  12. 28. A ___ field helps visualize differential equations.
  13. 29. ___ discontinuity. When the function approaches infinity at a certain point from both sides.
  14. 30. Derivative of position
  15. 32. ___ discontinuity. When the graph steps or jumps from one connected piece of the graph to another.
  16. 33. ___ point. A point on the graph of a function at which the derivative is either 0 or undefined.
  17. 35. ___ series are an infinite of terms expressed in terms of a function's derivatives at a point; used to approximate functions
  18. 37. Instantaneous rate of change at a point on a curve
  19. 38. ___ differentiation can help find dy/dx for relationships such as x^2 + y^2 = 1.
  20. 39. ___ integral. A calculation of area beneath a function, using infinitesimal slivers or stripes of the region. Yields a value.
  21. 40. ___ discontinuity. A hole in a graph.
  22. 42. ___ rule is used to find derivative of composite functions
  23. 43. The value a function approaches as the input approaches some value
  24. 45. ___ rule can find derivative of functions like 2x^2
  25. 46. The ___ theorem allows the computation of the limit of an expression by trapping the expression between two other expressions which have limits that are easier to compute.
  26. 48. ___ rate of change. The change in the value of a quantity divided by an elapsed time.
  27. 49. ___ of convergence. For a power series in one variable, it is the set of values of the variable for which the series converges.
  28. 50. ___ equation. Defines a group of quantities as functions of one or more independent variables called parameters.
Down
  1. 1. ___ test. A convergence test used when terms of a series contain factorials and/or nth powers.
  2. 2. ___ rule states that d(uv)/dx = u(dv/dx) + v(du/dx). Used to find the derivative of two functions multiplied together.
  3. 3. Second derivative of position
  4. 5. ___ series are Taylor series centered at x=0
  5. 7. ___ convergence. Describes a series that converges but does not converge absolutely.
  6. 10. The ___ line is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line.
  7. 11. L'___'s rule is used to evaluate limits that result in indeterminate expressions by taking the limit of the derivatives of the both the numerator and denominator.
  8. 13. ___ integral. A definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration.
  9. 14. ___'s method. Used to approximate solutions to differential equations that cannot be solved through separation of variables.
  10. 16. ___ integral. Integral expressed without limits and contains an arbitrary constant.
  11. 18. ___ method. Way to find the volume of objects of revolution. It’s a modification of the disc method for solid objects to allow for objects with holes.
  12. 19. ___ of variables. Method of solving differential equations.
  13. 21. ___ convergent. Describes a series that converges when all terms are replaced by their absolute values.
  14. 22. The ___ of a function f is a differentiable function F whose derivative is equal to the original function f.
  15. 24. To approach a finite value.
  16. 27. The ___ series diverges and is 1 + 1/2 + 1/3 + ... + 1/n + ...
  17. 31. The function to be integrated in an integral
  18. 34. ___ fractions. Process of writing any proper rational expression as a sum of proper rational expressions; method used in integration.
  19. 36. ___ series: Infinite series whose terms alternate between positive and negative.
  20. 39. ___ method. A method for calculating the volume of a solid of revolution when integrating along an axis "parallel" to the axis of revolution.
  21. 41. Fails to approach a finite value; opposite of converge.
  22. 44. Property of a function determined by taking the second derivative
  23. 47. The ___ logarithm, or ln(x) is the antiderivative of 1/x.
  24. 51. Abbreviation; If f is differentiable over an interval from a to b, there exists a number c such that f'(c) is equal to the average rate of change over the interval.