lim_(x rarr pi)cot(x)=? Choose 1 answer: (A) -1 (B) 0 (C) 1 (D) The limit doesn't exist.

Recall Definition of Cotangent: First, let's recall the definition of cotangent in terms of sine and cosine: cot(x) = cos(x) / sin(x) We need to find the limit of this function as x approaches pi.Evaluate Functions at x = pi: Evaluate the cosine and sine functions at x = pi: cos(pi) = -1 sin(pi) = 0Substitute Values into Cotangent Function: Substitute these values into the cotangent function: cot(pi) = cos(pi) / sin(pi) = -1 / 0 This expression shows that the function approaches negative infinity or positive infinity depending on the direction from which x approaches pi, because division by zero is undefined.Limit Does Not Exist: Since the sine function is zero at x = pi and the cosine function is negative, the cotangent function does not have a finite limit as x approaches pi. Instead, it approaches negative or positive infinity depending on the direction of approach, which means the limit does not exist.

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\lim _{x \rightarrow \pi} \cot (x)=?

\newline

Choose

1

answer:

\newline

(A)

-1

\newline

(B)

0

\newline

(C)

1

\newline

(D) The limit doesn't exist.

Recall Definition of Cotangent: First, let's recall the definition of cotangent in terms of sine and cosine: $\newline$ $\cot(x) = \frac{\cos(x)}{\sin(x)}$ $\newline$ We need to find the limit of this function as $x$ approaches $\pi$ .
Evaluate Functions at $x = \pi$ : Evaluate the cosine and sine functions at $x = \pi$ : $\cos(\pi) = -1$ $\sin(\pi) = 0$
Substitute Values into Cotangent Function: Substitute these values into the cotangent function: $\cot(\pi) = \frac{\cos(\pi)}{\sin(\pi)} = \frac{-1}{0}$ This expression shows that the function approaches negative infinity or positive infinity depending on the direction from which $x$ approaches $\pi$ , because division by zero is undefined.
Limit Does Not Exist: Since the sine function is zero at $x = \pi$ and the cosine function is negative, the cotangent function does not have a finite limit as $x$ approaches $\pi$ . Instead, it approaches negative or positive infinity depending on the direction of approach, which means the limit does not exist.