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Question #0138c

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Apr 16, 2017

# lim_(x->0)frac{1}{sin^3x-1/(x^3)}=0#

Explanation:

#lim_(x->0)frac{1}{sin^3x-1/(x^3)}#

Multiply the fraction by #color(blue)(frac{x^3}{x^3})# to get
#lim_(x->0)frac{x^3}{x^3sin^3x-1}#

By direct substitution, this gives:
#frac{color(red)(0)^3}{color(red)(0)^3sin^3 color(red)(0)-1}=0/-1 =0#

#:. lim_(x->0)frac{1}{sin^3x-1/(x^3)}=0#

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