Lim{h->0} (³√x+h)-(³√x)÷h ???

1 Answer
maganbhai P.
Mar 15, 2018

#1/3*x^(-2/3)#

Explanation:

We know that,
#color(red)(lim_(X toa)(X^n-a^n)/(x-a)=na^(n-1))#
#L=lim_(h to0)((x+h)^(1/3)-(x)^(1/3))/h#
Now, #h to0=>x+h tox#
#L=lim_((x+h)tox)((x+h)^(1/3)-(x)^(1/3))/((x+h)-x)#
#L=1/3*x^(1/3-1)=1/3*x^(-2/3)#

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