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Timur1234
@Timur1234
March 2022
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[tex] \lim_{n \to \ 0} \frac{(1-cos4x)}{2xtg2x} [/tex]
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Edelstein
Lim (1-cos(4*x))/(2*x*tg(2*x))=Lim ((1-cos(4*x))')/((2*x*tg(2*x))')=
=Lim (4*sin(4*x))/(2*tg(2*x)+4*x/((cos(2*x))^2)=
=Lim ((4*sin(4*x))')/((2*tg(2*x)+4*x/((cos(2*x))^2)')=
=Lim (16*cos(4*x))/(4/((cos(2*x))^2)+(4*(cos(2*x))^2)-4*x*2*cos(2*x)*2)/((cos(2*x))^4))=
=16*cos(0)/(4/(cos(0)^2)+(4*(cos(0))^2-0)/(cos(0))^4)=16/(4+4)=2.
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Answers & Comments
=Lim (4*sin(4*x))/(2*tg(2*x)+4*x/((cos(2*x))^2)=
=Lim ((4*sin(4*x))')/((2*tg(2*x)+4*x/((cos(2*x))^2)')=
=Lim (16*cos(4*x))/(4/((cos(2*x))^2)+(4*(cos(2*x))^2)-4*x*2*cos(2*x)*2)/((cos(2*x))^4))=
=16*cos(0)/(4/(cos(0)^2)+(4*(cos(0))^2-0)/(cos(0))^4)=16/(4+4)=2.