lim_(x rarr0)cot(x)=? Choose 1 answer: (A) -1 (B) 0 (C) 1 (D) The limit doesn't exist.

Understanding cotangent function: To solve the limit of cot(x) as x approaches 0, we need to understand the behavior of the cotangent function near 0. The cotangent function, cot(x), is defined as the reciprocal of the tangent function, so cot(x) = 1/tan(x).Behavior of cot(x) near 0: We know that tan(x) approaches 0 as x approaches 0. Since cot(x) is the reciprocal of tan(x), as tan(x) gets smaller and smaller, cot(x) will get larger and larger in magnitude. This means that the limit of cot(x) as x approaches 0 from the right (0+) will approach positive infinity, and from the left (0-) will approach negative infinity.Limit of cot(x) as x approaches 0: Because the behavior of cot(x) as x approaches 0 from the right is different from the behavior as x approaches 0 from the left, the limit does not exist. The function does not approach a single finite value from both sides.

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\lim _{x \rightarrow 0} \cot (x)=?

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Choose

1

answer:

\newline

(A)

-1

\newline

(B)

0

\newline

(C)

1

\newline

(D) The limit doesn't exist.

Understanding cotangent function: To solve the limit of $\cot(x)$ as $x$ approaches $0$ , we need to understand the behavior of the cotangent function near $0$ . The cotangent function, $\cot(x)$ , is defined as the reciprocal of the tangent function, so $\cot(x) = \frac{1}{\tan(x)}$ .
Behavior of cot( $x$ ) near $0$ : We know that $\tan(x)$ approaches $0$ as $x$ approaches $0$ . Since $\cot(x)$ is the reciprocal of $\tan(x)$ , as $\tan(x)$ gets smaller and smaller, $\cot(x)$ will get larger and larger in magnitude. This means that the limit of $\cot(x)$ as $x$ approaches $0$ from the right ( $0$ $3$ ) will approach positive infinity, and from the left ( $0$ $4$ ) will approach negative infinity.
Limit of $\cot(x)$ as $x$ approaches $0$ : Because the behavior of $\cot(x)$ as $x$ approaches $0$ from the right is different from the behavior as $x$ approaches $0$ from the left, the limit does not exist. The function does not approach a single finite value from both sides.