Question

find the limit of this​

Answer 1

$\huge{\underline{\underbrace{\mathcal\color{gold}{Answer}}}}$

$\bold{Lt_{_{x\longrightarrow{0}}}\dfrac{3sinx^{0}-sin(3x)^{0}}{x^{3}}}$

=$\bold{Lt_{_{x\longrightarrow{0}}}\dfrac{4sin^{3}x^{0}}{x^{3}}  }$ 

=$\bold{Lt_{_{x\longrightarrow{0}}}\dfrac{4sin^{3}(\dfrac{\pi}{180}x)}{x^{3}}   }$ 

=$\bold{Lt_{_{x\longrightarrow{0}}}\dfrac{4sin^{3}(\dfrac{\pi}{180}x)}{x^{3}}×\dfrac{(\dfrac{\pi}{180})^{3}}{(\dfrac{\pi}{180})^{3}}    }$ 

=$\bold{(\dfrac{\pi}{180})^{3} ~~ Lt_{_{x\longrightarrow{0}}}\dfrac{4sin^{3}(\dfrac{\pi}{180}x)}{x^{3}(\dfrac{\pi}{180})^{3} } }$

• ($\because$$\tt{Lt_{_{x\longrightarrow{0}}}\dfrac{sin^{3}(\dfrac{\pi}{180}x)}{x^{3}(\dfrac{\pi}{180})^{3} } =1   }$)

=$\bold{(\dfrac{\pi}{180})^{3}×4   }$

=$\bold{\blue{4(\dfrac{\pi}{180})^{3} }  }$(ANS)

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