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absolute convergence while we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with
related rates in this section we will discussed for application of implicit differentiation for these related rates problems usually its best to
suppose that x x t and y y t and differentiate the following equation with respect to
interpretations of derivativesexample find out the equation of the tangent line
simple derivativesexample differentiate following 5x3 - 7 x 15 f x 5 y x 5solution here with the first function were being asked
alternating series test - sequences and seriesthe final two tests that we looked at for series convergence has needed that all the terms in the
determine yprime for xy 1 solution there are in fact two solution methods for this problemsolution 1 it is the simple way of doing the problem
implicit differentiation to this instance weve done quite a few derivatives however they have all been derivatives of function of the form y f x
comparison test assume that we have two types of series suman and sumbn with an bn ge 0 for all n and an le bn for all n thena if sumbn is
differentiate following functionsa f x 2 x5 cosh xb h t sinh t t 1solutiona f prime x 10x4 cosh x 2x5 sinh xb hprime t t 1 cosh t -
a radiograph is made of an object with a width of 3 mm using an x-ray tube with a 2 mm focal spot at a source-to-film distance of 100 cm the object
telescoping series its now time to look at the telescoping series in this section we are going to look at a series that is termed a
series - special series in this part we are going to take a concise look at three special series in fact special may not be the correct term
series - convergencedivergencein the earlier section we spent some time getting familiar with series and we briefly explained convergence and
inverse sine lets begin with inverse sine following is the definition of the inverse siney sin -1 x harr
derivatives of inverse trig functions now we will look at the derivatives of the inverse trig functions to derive the derivatives of inverse trig
obligatory applicationinterpretation problem next we need to do our obligatory applicationinterpretation problem so we dont forget about themexample
differentiate following functionsa r w 4w - 5 log9 wb f x 3ex 10x3 ln xsolution a it will be the only example which
logarithm functions now lets briefly get the derivatives for logarithms in this case we will have to start with the following fact regarding
theorem if an is bounded and monotonic then an is convergent be cautious to not misuse this theorem it does not state that if a sequence is
determine if the following sequences are monotonic andor boundeda -n2infinn0b -1n1infinn1c 2n2infinn5solution-n2infinn0this sequence is a
monotonic upper bound and lower boundgiven any sequence an we have the following terminology1 we call or denote the sequence increasing if an
derivatives of exponential and logarithm functions the next set of functions which we desire to take a look at are exponential amp logarithm
differentiate following functions g x 3sec x -10 cot x solution there
sequenceslet us start off this section along with a discussion of just what a sequence is a sequence is nothing much more than a list of numbers