Question

evaluate lim x π /4 sin2x^tan^2 2x

Answer 1

as x tends to...?

Answer 2

just for clarity, is this what you are asking:
\[\lim_{x \rightarrow \pi/4}(\sin 2x)^{\tan^{2} 2x}\]

Answer 3

\[\lim_{x \rightarrow \pi/4}(\sin2x)^{\tan^2 2x}=\lim_{x \rightarrow \pi/4}(1-(sinx -\cos x)^2)^{\tan^2 2x}\]
\[\lim_{x \rightarrow \pi/4}(1-(1-\sin2x))^{\frac{\sin^22x}{(1-\sin2x)(1+2\in2x)}}\]\[(\lim_{x \rightarrow \pi/4}(1-(1-\sin2x))^\frac 1{1-\sin2x})^{\lim_{x \rightarrow \pi/4}\frac {\sin^22x}{1+\sin2x}}\]\[e^{1/2}\]

Answer 4

hello got it???

Answer 5

i used the formula..\[\lim_{y \rightarrow 0}(1+y)^{\frac1y}=e\]

Answer 6

here y=1-sin2x