Calculus crossword

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Across
  1. 3. expansion of a rational fraction is an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator
  2. 5. named after Gottfried Wilhelm Leibniz, generalizes the product rule
  3. 6. A fundamental concept in calculus and analysis concerning the behavior of that function near a particular input
  4. 9. A function of one real variable whose derivative exists at each point in its domain
  5. 11. a numerical method to solve first order first degree differential equation with a given initial value
  6. 18. derivative of Sinx
  7. 19. This makes a function not continuous that jumps from one point to another
  8. 20. finds the area under a curve
  9. 21. the counterpart to the chain rule for differentiation
  10. 25. states that is [a,b] is continuous, (a,b) is differentiable, f(a)=f(b), then there must be a point where f’(c)=0
  11. 27. used to determine if a POI in increasing or decreasing
  12. 32. often simplified by saying log
  13. 33. a function that has no discontinuities in it is called a function
  14. 35. a technique for approximating the integral of a function by using trapezoids
  15. 38. A formula for finding the derivative of a function that is the ratio of two functions
  16. 39. A function f defined on some set X with real or complex values
  17. 41. Finding the integral of a function at any point i.e. 12x2+C
  18. 42. An infinite series whose terms alternate between positive and negative
  19. 43. rule used to take the derivatives of functions
  20. 45. a line that continually approaches a given value but never touches it
  21. 47. a method used to differentiate functions by employing the logarithmic derivative of a function f
  22. 48. the highest value a function attains
  23. 49. The velocity of an object in motion at a specific point in time
  24. 50. abf(x)dx=F(b)−F(a)
Down
  1. 1. problems involve two variables that change at the same time
  2. 2. finding the maximum or minimum possible value of a function
  3. 4. the limit of a definite integral as an endpoint of the interval(s) of integration
  4. 7. a graphical representation of the solution of a first derivative of a function
  5. 8. used to determine if a POI is an absolute minimum of maximum
  6. 10. determines whether a graph is concave or convex
  7. 12. the non negative value of x without regard to its sign
  8. 13. another method for integration by parts
  9. 14. A(x) = cxf(t)dt
  10. 15. form of shorthand used to give a concise expression for a sum of the values of a variable
  11. 16. the lowest value a function attains
  12. 17. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
  13. 22. logarithm simplified version is ln
  14. 23. The name for a function which is being integrated
  15. 24. A formula used to find the derivatives of products of two or more functions
  16. 26. uses derivatives to help evaluate limits involving indeterminate forms
  17. 28. point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0
  18. 29. States that if a real valued function f is continuous on the closed interval [a,b], then f must attain a maximum and a minimum, each at least once
  19. 30. ∫udv = uv ∫ vdu
  20. 31. the mathematical study of continuous change
  21. 34. A term that refers colloquially to some quantities that cannot be expressed by a single number (a scalar), or to elements of some vector spaces
  22. 36. If a function is not continuous at a point in its domain, one says that it has a _____ there
  23. 37. equation which describes the slope of any function at a point
  24. 40. a differentiable function F whose derivative is equal to the original function f
  25. 44. a formula for computing the derivative of the composition of two or more functions
  26. 46. a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann