Question

lim x→0 (sin⁴ x)/x

Answer 1

L'Hopital's rule will work here.

Answer 2

Or, more simply, use the rule that the limit of the product is the product of the limits.\[\lim_{x→0 }\frac{ (\sin⁴ x)}{x}=\lim_{x→0 }\sin^3x \lim_{x→0 }\frac{ (\sin x)}{x}=0\]

Answer 3

Recall that \[\lim_{x \rightarrow 0}\frac{sinx}{x}=1\]

Answer 4

ok

Answer 5

so should it be 1⁴?

Answer 6

No. How did you get that?

Answer 7

well the identity gives us one

Answer 8

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.

Answer 9

oh I follow now

Answer 10

No sweat. Do math every day.

Answer 11

thank you, I just didn't know I could separate to make that identity thanks a lot for your help

Answer 12

Just remember the rules, and figure out how to make the problem look like something that you can solve.

Answer 13

dually noted. thanks again.