A Treatise On Infinitesimal Calculus: Containing Differential And Integral ... 1

Bartholomew Price

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Evaluate a?* when a? = 0.
Let y = X', .'. logy = 0? logo?; Digitized by Google ia8.] INDBTBRMINATB QUANTITIES. 211 and by Article 126, Ex. 2, ^ log ^ =: 0, when a? = ; therefore log y = ; and since log 1=0; therefore y = j^' =1, when j? = 0.
Ex. 2. Eyaluate xx, when ^ = oo .
I Let y = j?«^ .-. logy = -^ = ^, when a?= oo; = 1 = 0, .
a?
1 .-. y = XX =z I, when a? = oo .
Ex. 3. Evaluate (1 + ax)x, when jr = 0, and when jr = oo .
Let y = (1 -f ax)x ; , Alog(l + a^) u ft .-. l>. -f 0.-^^ when x = 0....
Let y^^^^'"-^^'"+'-'^^'"Y, . I ^ log («!** + fla'^^-h .>■ + fln**^) - log » ^ if^_Q a? 0' — **log^i'^i''*"*"^log^*^***'^" ••• +» log On.aw"* = log(aia2...«n), if ^ = 0.
Therefore |^i--H^»-+ »>> "f ^>^-|-'^ ^^^...^^ if ^^0.
/Google E e :2 Digitized by ^ 212 EXPANSION OF FUNCTIONS.

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