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Proof of Root Test Firstly note that we can suppose without loss of generality that the series will initiate at n = 1 as we've done for all our series test proofs. As well n
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Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2
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Vector Arithmetic In this part we need to have a brief discussion of vector arithmetic. Addition We will begin with addition of two vectors. Thus, given the vectors a
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Find out all the critical points for the function. Solution To determine the derivative it's probably simple to do a little simplification previous to we in fact diffe
The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
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