Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Question #0138c

1 Answer

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#

Related questions

See all questions in Determining Limits Algebraically

Impact of this question

994 views around the world

You can reuse this answer
Creative Commons License