Ashley W's View on Calculus
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| Define it. | Understand it. | Do it. | Apply it. |
Limit | A limit is an area of a graph that has both sides of the graph heading towards or where the graph is heading. | Yes I do. | Good to go, | Ready for blast off! |
Definite Integral | Area of a section of the graph. | Yes I do. | Good to go, | Ready for blast off! |
Derivative | Instantaneous rate of change or the slope of a point on a graph. | Yes I do. | Good to go, | Ready for blast off! |
Indefinite Integral | | | | |
The three concepts of calculus that we studied and went over so far are Derivatives, Definite Integrals, and Limits. The distinctions between the three aren’t hard when put into human translation. A derivative is the instantaneous rate of change or the slope of a point on a graph. Definite integrals are the area of a section of the graph. Lastly, a limit is a point on a graph where both sections are heading. So, if there is a hole in a function the limit at that point still excesses because both sides of the function is heading towards that given value. If there is a step in a graph or function, then there is no limit becuase both sides aren't heading towards a single giving value. If the graph as an asymptote in which both sides are heading to positives infinity or negative infinity, then the limit is positive or negative infinity. But, this will depend on the teacher you have.
The techniques that we learn in calculating or estimating these concepts are simple. For estimating derivatives we take the closest points to the original point on the graph and find the rate of change or the slope by using the slope formula: delta y/delta x or(y1-y20/(x1-x2). To find the definite integrals, you use the trapezoid method. The Trap. rule is (1/2b1+b2+b3+b4+1/2b5)w; which is half of the base one plus all the other bases and the half of the last one times the w. Lastly, to find the limit is the finger test; does it meet at a point?
Modified on September 20, 2006 at 6:29 PM