Question

by changing variables using the fact that lim theta-->0 sin theta / theta = 1 ......... fine the limit using the squeeze theorem. lim x--> 0 x^2/sing^2(4x)

Answer 1

x\[\lim x \rightarrow 0 x ^{2}/\sin ^{2}4x\]

Answer 2

please help!!!

Answer 3

Is it asking to find the limit using the squeeze theorem or manipulate algebraically and evaluate using lim ->x sinx/x?

Answer 4

If algebraically, its very easy to show the limit.\[\lim_{x \rightarrow 0} \frac {x^2}{\sin^2 (4x)} = \lim_{x \rightarrow 0} \frac {x}{\sin (4x)}\times \lim_{x \rightarrow 0} \frac {x}{\sin (4x)}\]\[\lim_{x \rightarrow 0} \frac {\sin ax}{x} = a \rightarrow \lim_{x \rightarrow 0} \frac {x}{\sin ax} = \frac {1}{a}\]\[\lim_{x \rightarrow 0} \frac {x}{\sin (4x)}\times \lim_{x \rightarrow 0} \frac {x}{\sin (4x)} = \frac {1}{4} \times \frac {1}{4}\]\[\lim_{x \rightarrow 0} \frac {x^2}{\sin^2 (4x)} = \frac {1}{16}\]