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position vectorthere is one presentation of a vector that is unique in some way the presentation of the v a1a2a3 that begins at the point a
extrema note as well that while we say an open interval around x c we mean that we can discover some interval a b not involving the endpoints
definition1 we say that fx consist an absolute or global maximum at x c if f x le f c for every x in the domain we are working on2 we
minimum and maximum values several applications in this chapter will revolve around minimum amp maximum values of a function whereas we can all
critical point of exponential functions and trig functionslets see some examples that dont just involve powers of xexample find out all the
critical point definition we say that x c is a critical point of function fx if f c exists amp if either of the given are truef prime c
two cars begin 500 miles apart car a is into the west of car b and begin driving to the east that means towards car b at 35 mph amp at the
vectors this is a quite short section we will be taking a concise look at vectors and a few of their properties we will require some of this
estimating the value of a seriesone more application of series is not actually an application of infinite series its much more an application of
fourier series - partial differential equationsone more application of series arises in the study of partial differential equations one of the
series solutions to differential equationshere now that we know how to illustrate function as power series we can now talk about at least some
application of rate changebrief set of examples concentrating on the rate of change application of derivatives is given in this
important formulasd ab dx 0 important formulasd ab dx 0
differentiate y x xsolution weve illustrated two functions similar to this at this pointd xn dx nxn
interpretation of the second derivative now that weve discover some higher order derivatives we have to probably talk regarding an interpretation of
determine yprimeprime determine yprimeprime
determine the second derivative for following
interval of convergenceafter that secondly the interval of all xs involving the endpoints if need be for which the power series converges is termed
example determines the first four derivatives for
radius of convergencewe will be capable to illustrate that there is a number r so that the power series will converge for x - a lt r and will diverge
higher order derivatives lets begin this section with the given function
power series we have spent quite a bit of time talking about series now and along with just only a couple of exceptions weve spent most of that time
strategy for series now that we have got all of our tests out of the way its time to think regarding to the organizing all of them into a general set
root test- sequences and seriesthis is the final test for series convergence that were going to be searching for at like with the ratio test this
proof for absolute convergencevery first notice that an is either an or it is - an depending upon its sign the meaning of this is that we can