Question

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Answer 1

Step-by-step explanation:

EXPLANATION.

$\sf \implies \displaystyle \lim_{x \to 0} \bigg(\dfrac{x^{2} }{sinx^{2} } \bigg)$

As we know that,

Formula of :

$</p><p>\sf \implies \displaystyle \lim_{x \to 0} \bigg(\dfrac{x}{sin(x)} \bigg) = 1.$

Using this formula in the equation.

We can write equation as,

$\sf \implies \displaystyle \lim_{x \to 0} \bigg( \dfrac{x}{sin(x)} \bigg)^{2} = (1)^{2} = 1.$

$\sf \implies \displaystyle \lim_{x \to 0} \bigg(\dfrac{x^{2} }{sinx^{2} } \bigg) = 1.$

MORE INFORMATION.

(1) = eˣ = 1 + x + x²/2! + x³/3! + . . . . .

(2) = e⁻ˣ = 1 - x + x²/2! - x³/3! + . . . . .

(3) = ㏒(1 + x) = x - x²/2 + x³/3 - . . . . .

(4) = ㏒(1 - x) = - x - x²/2 - x³/3 - . . . . .

(5) = aˣ = 1 + (x ㏒ a) + (x ㏒ a)²/2! + (x ㏒ a)³/3! + . . . . .

(6) = sin x = x - x³/3! + x⁵/5! - . . . . .

(7) = cos x = 1 - x²/2! + x⁴/4! - . . . . .

(8) = tan x = x + x³/3 + 2x⁵/15 + . . . . .

Answer 2

Step-by-step explanation:

I hope this answer is correct.