Calculus

Across

2. (uv)= u'v + uv'
5. the region bounded by the function we're working with vertical lines representing the function's bounds and the x-axis
6. a first-order numerical procedure for solving ordinary differential equations with a given initial value
7. straight line that just touches the curve at that point
8. simple operation in which a number is divided
11. a numerical quantity that is not a whole number
13. simple operation in which a number is taken away from another number
16. branch of mathematics that deals with the finding and properties of derivatives and integrals of functions by methods originally based on the summation of infinitesimal differences
18. quantity that expresses the extent of a region on the plane or on a curved surface
22. Obtaining the derivative of a function
27. The slope of the line tangent to the function
29. When the graph of the function is continuous
30. lowest point of a specified interval of a graph
31. a graphical representation of the solutions to a first-order differential equation of a scalar function
34. a relation of the form R = 0 where R is a function of several variables
37. the graph lies below its tangent lines
38. a number greater than any assignable quantity or countable number
41. process of combining matrices vectors or other quantities under specific rules to obtain their product
43. number that is expressed in terms of the square root of a negative number represented by i
44. Where the function changes from concave up to concave down or vice versa
45. a value that a function approaches the output for the given input values
46. the magnitude of a real number without regard to its sign
48. quantity representing the power to which a given number or expression is to be raise
49. for a given planar arc between two endpoints there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints

Down

1. a mathematical object that can be interpreted as an area or a generalization of area
3. highest point of a specified interval of a graph
4. cool math teacher that gives people doughnuts occasionally
5. a mathematical function that is the inverse of the cosine function
9. f'(g(x))g'(x)
10. a line that continually approaches a given curve but does not meet it at any finite distance
12. A point at which the graph of the function is not continuous
14. an integration rule that evaluates the area under the curves by dividing the total area into smaller trapezoids rather than using rectangles
15. a mathematical function that is the inverse of the tangent function
17. the change in velocity over the change in time
19. simple operation in which a number is added onto another number
20. yummy treats that are given by cool math teacher occasionally
21. branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles
23. a mathematical function that is the inverse of the sine function
24. Highest point of a function
25. Finding the derivative of the numerator and denominator to evaluate the limit of a function
26. when the two-sided limit doesn't exist because the one-sided limits aren't equal
28. The rate of change in the position of an object
32. the graph lies above its tangent lines
33. a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface
35. a point of a curve at which a change in the direction of curvature occurs
36. Lowest point of a function
39. Rates of change are related by differentiation
40. a differentiable function F whose derivative is equal to the original function f
42. a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero
47. a point at which two branches of a curve meet such that the tangents of each branch are equal