Given #(sin^2(x^2))/(x^4)# how do you find the limit as x approaches 0?

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Answer 1 · 2016-08-04T15:56:54

1

we'll use well known limit
#= lim_{z to 0} (sin(z))/(z) = 1#

#lim_{x to 0} (sin^2(x^2))/(x^4)#

#= lim_{x to 0} (sin(x^2))/(x^2) (sin(x^2))/(x^2)#

let # y = x^2#

#= lim_{y to 0} (sin(y))/(y) (sin(y))/(y)#

because both limits exist, as stated above, we can separate them out
#= lim_{y to 0} (sin(y))/(y) * lim_{y to 0} (sin(y))/(y)#

#= 1 * 1 = 1#