DERIV
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DERIV
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Calculus
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http://course-notes.org/Calculus
DERIV
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CALC
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CALC
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Multi-Variable Calculus summary
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Calculus II
Subject:
calculus, calculus, calculus
derivative
slope
second derivative test
Calculus
Series
Subject:
CALCULUS BC SERIES SERIES: PARTIAL SUMS: If (that it, the sequence of partial sums converges), then is the sum of the series so . In this case is CONVERGENT and has sum s. Thus a series converges if its sequence of partial sums converges. [Sec 11.2: p 2] EXAMPLES Does the series converge or diverge? 1. Partial sums: so, and thus the series converges and has sum = 1 2. Harmonic series: Partial sums: Thus the series diverges. [Sec 11.2: p3] 3. Here, (using partial fractions) Partial sum: Thus the series converges and has sum = 5. This is an example of a TELESCOPING SERIES.
Sequences
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CALCULUS BC NOTES: SEQ 11.1 (revised 2010) SEQUENCE: a list of numbers OR a function whose domain is the set of positive integers FIND FIRST 5 TERMS OF EACH SEQUENCE: 1) 2) 3) LIMIT of a SEQUENCE: (p 695) If where L is a finite number, the sequence CONVERGES. If no limit, the sequence DIVERGES. THEOREM: If (p 696) [Sec 11.1: p 2] FIND THE LIMIT OF EACH SEQUENCE. TELL WHETHER SEQUENCE CONVERGES OR DIVERGES. 4) 5) INCREASING/DECREASING SEQUENCES: increases if for all n decreases if for all n BOUNDED SEQUENCE : (p 700) Above: for all Below: for all [Sec 11.1: p 3] MONOTONIC SEQUENCE: always increasing or always decreasing
AP CALC integrations
Subject:
Review 6 Name: __________________________________________________ AP Calculus BC Date: ______________________________ Period: _____ Find the area between and . Find the area between , and . (Use a single integral!) Find the volume of the region bounded by , and revolved about the -axis. (Use the method of disks!) Find the volume of the region bounded by , and revolved about the -axis. (Use the method of washers!) Find the volume of the region bounded by from , and revolved about . (Use the method of shells!) Find the arc length for the specified portion of each curve. An object is dropped from a height of 100 feet. Find its velocity when it hits the ground.
Trig functions
Subject:
Review : Trig Functions The intent of this section is to remind you of some of the more important (from a Calculus standpoint?) topics from a trig class. One of the most important (but not the first) of these topics will be how to use the unit circle. We will actually leave the most important topic to the next section. First let?s start with the six trig functions and how they relate to each other. Recall as well that all the trig functions can be defined in terms of a right triangle. From this right triangle we get the following definitions of the six trig functions. Remembering both the relationship between all six of the trig functions and their right triangle definitions will be useful in this course on occasion.
AP inversfunction
Subject:
Review : Inverse Functions In the last example from the previous section we looked at the two functions and and saw that and as noted in that section this means that there is a nice relationship between these two functions. Let?s see just what that relationship is. Consider the following evaluations. In the first case we plugged into and got a value of -5. We then turned around and plugged into and got a value of -1, the number that we started off with. In the second case we did something similar. Here we plugged into and got a value of , we turned around and plugged this into and got a value of 2, which is again the number that we started with. Note that we really are doing some function composition here. The first case is really, and the second case is really,
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