Solve: lim_((x,y)→(0,0)) ((1−cos((√(10xy))))/(3.y.sin(22x))) Ans.: (5/(66)) Step by step, please!


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Question Number 205114 by 2kdw last updated on 09/Mar/24

$S o l v e :$ ${l i m}_{(x, y) \to (0, 0)} \frac{1 - c o s (\sqrt{10 x y})}{3 . y . s i n (22 x)}$ $A n s . : \frac{5}{66}$ $S t e p b y s t e p, p l e a s e!$
	Answered by MM42 last updated on 09/Mar/24

	${l i m}_{(x, y) \to (0, 0)} \frac{2 {s i n}^{2} (\frac{\sqrt{10 x y}}{2})}{3 y s i n 22 x}$ $\sim= {l i m}_{(x, y) \to (0, 0)} \frac{2 \times {(\frac{s i n \frac{\sqrt{10 x y}}{2}}{\frac{\sqrt{10 x y}}{2}})}^{2} \times \frac{10 x y}{4}}{3 y \times (\frac{s i n 22 x}{22 x}) \times 22 x}$ $= \frac{5 x y}{66 x y} = \frac{5}{66} ✓$
	Commented by 2kdw last updated on 09/Mar/24
	Thanks Sir
	Commented by lepuissantcedricjunior last updated on 12/Mar/24

	$g o o d!!!$
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