fraction, Mathematics

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Definition and fact of the shape of a graph, Definition 1.   Given any ...

Definition 1.   Given any x 1  & x 2   from an interval  I with x 1 2  if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2.   Given any x 1  & x 2  from an interval

Example of convergent or divergent - comparison test, Determine if the subs...

Determine if the subsequent series is convergent or divergent. Solution As the cosine term in the denominator doesn't get too large we can suppose that the series term

Applied Math, Calucations of gradients find f Graph some level curve f=cons...

Calucations of gradients find f Graph some level curve f=const. f=9x^2 = 4y^2

Determines the first four derivatives of y = cos x, Example    determines t...

Example    determines the first four derivatives for following.                                                                  y = cos x Solution: Again, let's just do so

Expect mean, Your factory has a machine for drilling holes in a sheet metal...

Your factory has a machine for drilling holes in a sheet metal part.  The mean diameter of the hole is 10mm with a standard deviation of 0.1mm. What is the probability that any

Time and Work, A and B can finish a piece of work in 16 days and 12 days re...

A and B can finish a piece of work in 16 days and 12 days respectively.A started a work and worked at it for 2 days.He was then joined by B.Find the total time taken to finish the

Number of permutations of ''n'' dissimilar things , Finding the numbe...

Finding the number of Permutations of 'n' dissimilar things taken 'r' at a time:  After looking at the definition of permutations, we look at how to evolve a

Compute the value of the following limit, Compute the value of the followin...

Compute the value of the following limit. Solution: Notice as well that I did say estimate the value of the limit.  Again, we will not directly compute limits in this sec

How to solve lim 1-cos(x)/1-cos(4x) as x tends to zero, Use L''hopital''s r...

Use L''hopital''s rule  since lim X-->0  1-cos(x)/1-cos(4x)  is in the indeterminate form 0/0 when we apply the limt so by l''hoptital''s rule differentiate the numerator and den

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