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limit definition of 1/x?
I need the limit definion of 1/x
3 Answers
- Anonymous8 years agoFavorite Answer
Ask clearly: question makes no sense as stated.
- ?Lv 78 years ago
limit definition of a derivative i take it...
lim h-->0 [f(x+h) - f(x)] / h
[1/(x+h) - 1/x] / h
Find common denominator:
[(x - (x+h))/(x)(x+h)] / h
(x - x - h) / (x)(x+h)(h)
(-h) / (x)(x+h)(h)
Cancel an h:
-1 / (x)(x+h)
Take limit as h-->0
-1 / (x)(x+0)
= -1/x^2
Check by direct diff using power rule:
d/dx x^n
= nx^(n-1)
So:
d/dx x^-1 = -1x^-2 = -1/x^2
Good to go. rock on
