Roots and powers

You remember, of course, that xxx = and xxxxx = x, sojP xx = xxxxxxxxx = x. It is also easy to see that x /x = x. The general formulas are 

For the case m = n with x 51 0, the last result implies that From Eq. (3.29) with m — n. 

Remember that l/oo = 0, while 1/0 = oo. Dividing by zero used to send some older computers into a tizzy. 

Consider a more complicated expression, for example, a ratio of polynomials 

In the limit as x oo, x becomes negligible compared to x, as does any constant term. Therefore, 

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Integral E qjonents (Powers and Roots) If m and n are positive integers and a, h are numbers or funedious, then the fohowiug properties hold ... 

Scientific notation and decimals (integral powers and roots of base 10). 

Arithmetic, Powers, and Roots CHAPTER 3 MATH FOR CIVIL SERVICE TESTS... 

Why discuss these two macros here, when they achieve the same purpose, while one is so much simpler than the other Ihe reason is that they are not quite equivalent. For an array of numbers, defined and stored as then-values, macros such as Power and Root are our first choice, since they are indeed simpler to read as well as faster to execute. However, they have an Achilles heel since they modify one cell at the time, in an unspecified order, they are not reliable when the cell values are mutually dependent. 

Verify that repeated use of the Power and Root (or Powerl and Rootl) macros now does lead to computational errors with relative values smaller than 10 15. This final example illustrates that, while the spreadsheet always (and automatically) treats data as double precision, the mathematical operations in VBA must be told specifically to do so ... 

Another important set of numerical operations is the taking of powers and roots. If X represents some number that is multiplied by itself n — 1 times so that there are n factors, we represent this by the symbol x", representing x to the nth power. For example,... 

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