anonymous
  • anonymous
lim x→0 (sin⁴ x)/x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
L'Hopital's rule will work here.
anonymous
  • anonymous
Or, more simply, use the rule that the limit of the product is the product of the limits.\[\lim_{x→0 }\frac{ (\sin⁴ x)}{x}=\lim_{x→0 }\sin^3x \lim_{x→0 }\frac{ (\sin x)}{x}=0\]
anonymous
  • anonymous
Recall that \[\lim_{x \rightarrow 0}\frac{sinx}{x}=1\]

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anonymous
  • anonymous
ok
anonymous
  • anonymous
so should it be 1⁴?
anonymous
  • anonymous
No. How did you get that?
anonymous
  • anonymous
well the identity gives us one
anonymous
  • anonymous
Yeah, but the other limit \[\lim_{x \rightarrow0}\sin^3x =0\] is also a factor, and sends the limit of the product to zero. One times zero is zero.
anonymous
  • anonymous
oh I follow now
anonymous
  • anonymous
No sweat. Do math every day.
anonymous
  • anonymous
thank you, I just didn't know I could separate to make that identity thanks a lot for your help
anonymous
  • anonymous
Just remember the rules, and figure out how to make the problem look like something that you can solve.
anonymous
  • anonymous
dually noted. thanks again.

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