how can i solve : lim { ( (cubic root x) -1 ) / x } , when x->0 ?

Answer 1

lim { ( (cubic root x) -1 ) / x } , when x->0
= lim -1/x, x->0
= ±∞

Answer 2

lim { ( (cubic root x) -1 ) / x } , when x->0
(x^1/3-1)/x
The limit is infinity because you have -1/0. This is not an indeterminate case; rather it is undefined.

As x --> 0 from the right, y approaches - infinity and as x --> 0 from the left, y approaches + infinity.

Answer 3

It does not exist, or is undefined, since near 0, the function increases without bounds. If the limit of the numerator and denominator where both either infinite or zero. you could use L'Hospital's Rule, but not in this case.

Answer 4

a) The shrink is an indeterminate formulation 0/0 b) The shrink while y has a tendency to one million : lim(y-one million)/(y^3 -one million) has a similar difficulty. yet right here we are in a position to divide numerator and denominator by skill of (y-one million) and acquire: lim one million/(y^2 + y + one million) and the respond is one million/3 c) Now you manage your shrink: lim(x^(one million/3) -one million )/(x-one million) substitute the variable x by skill of y^3 and you gets lim(y-one million)/(y^3-one million) and the respond is acquire as defined in b)

Answer 5

add the additive inverse of 1 to the crx then divide by -.01