lim _{x rightarrow frac{3 pi}{2}} frac{cos x}{sin x-1}=

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Step:1 ：We are given the limit function (lim _{x rightarrow frac{3 pi}{2}} frac{cos x}{sin x-1})Step:2 ：To find the limit of a function as x approaches a certain value, we substitute the value of x into the function.Step:3 ：Substituting (frac{3 pi}{2}) into the function, we get (frac{cos(frac{3 pi}{2})}{sin(frac{3 pi}{2})-1})Step:4 ：This simplifies to (frac{0}{0-1}), or 0.Step:5 ：Therefore, the limit of the function as x approaches (frac{3 pi}{2}) is 0.Step:6 ：Final Answer: (boxed{0})

Answer

Step: 1 ：We are given the limit function (lim _{x rightarrow frac{3 pi}{2}} frac{cos x}{sin x-1})Step: 2 ：To find the limit of a function as x approaches a certain value, we substitute the value of x into the function.Step: 3 ：Substituting (frac{3 pi}{2}) into the function, we get (frac{cos(frac{3 pi}{2})}{sin(frac{3 pi}{2})-1})Step: 4 ：This simplifies to (frac{0}{0-1}), or 0.Step: 5 ：Therefore, the limit of the function as x approaches (frac{3 pi}{2}) is 0.Step: 6 ：Final Answer: (boxed{0})

$\lim _{x \rightarrow \frac{3 \pi}{2}} \frac{\cos x}{\sin x-1}=$

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