Question

limit x mendekati 0 dari 3x²/2 sin²x adalah

Answer 1

Answer:

$\lim_{x\to0}\frac{3x^2}{2\:sin^2x}=3/2$

Step-by-step explanation:

Formula used:

$\bf{\lim_{x\to0}\frac{sinx}{x}=1}$

$\lim_{x\to0}\frac{3x^2}{2\:sin^2x}$

$=\lim_{x\to0}\frac{3/2}{sin^2x/x^2}$

$=\frac{\lim_{x\to0}(3/2)}{\lim_{x\to0}(sin^2x/x^2)}$

$=\frac{\lim_{x\to0}(3/2)}{\lim_{x\to0}(sinx/x)^2}$

$=\frac{\lim_{x\to0}(3/2)}{(\lim_{x\to0}sinx/x)^2}$

$=\frac{3/2}{(1)^2}$

$=3/2$

Answer 2

The value of$\lim_{x \to 0} \dfrac{3x^{2} }{2\sin ^{2}x}=\dfrac{3}{2} .$

Step-by-step explanation:

We have,

$\lim_{x \to 0} \dfrac{3x^{2} }{2\sin ^{2}x}$

To find, the value of$\lim_{x \to 0} \dfrac{3x^{2} }{2\sin ^{2}x}$= ?

$\lim_{x \to 0} \dfrac{3x^{2} }{2\sin ^{2}x}$

=$\dfrac{3}{2} \lim_{x \to 0} \dfrac{x^{2} }{\sin ^{2}x}$

$=\dfrac{3}{2} \lim_{x \to 0} \dfrac{1 }{\dfrac{\sin ^{2}x}{x^{2}} }$

$=\dfrac{3}{2} \lim_{x \to 0} \dfrac{1 }{(\dfrac{\sin x}{x})^{2}  }$

$=\dfrac{3}{2} \lim_{x \to 0} \dfrac{1}{1} }$

[ ∵ $\lim_{x \to 0} \dfrac{\sin x}{x}=1$]

= $\dfrac{3}{2}$

Hence, the value of$\lim_{x \to 0} \dfrac{3x^{2} }{2\sin ^{2}x}=\dfrac{3}{2} .$