Find the limit when X approaches zero 2xsinx/1-cosx

asked Aug 20, 2022 153k views

1 vote

Find the limit when X approaches zero
2xsinx/1-cosx

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Answer:

Explanation:

$Lim_(x \to 0)(2 x\sin x)/(1-\cos x)$

$=Lim_(x \to 0)(2 x\sin x)/(1-\cos x)* (1+\cos x)/(1+\cos x)$

$=Lim_(x \to 0)(2 x\sin x(1+\cos x) )/(1^2 -\cos^2 x)$

$=Lim_(x \to 0)(2 x\sin x(1+\cos x) )/(1 -\cos^2 x)$

$=Lim_(x \to 0)(2 x\sin x(1+\cos x) )/(sin^2 x)$

$=Lim_(x \to 0)(2x(1+\cos x) )/(sin x)$

$=Lim_(x \to 0) 2(1+\cos x) * (1)/(Lim_(x \to 0)(sin x)/(x))$

$=2(1+\cos 0) * 1$

= 2(1+1)

= 2(2)

$\therefore Lim_(x \to 0)(2 x\sin x)/(1-\cos x)= 4$

Goseib answered Aug 27, 2022

6.3k points

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