lim_(x rarr(pi)/(4))cot(x)=? Choose 1 answer: (A) (sqrt2)/(2) (B) 1 (C) sqrt2 (D) The limit doesn't exist.

Recalling the definition of cotangent: First, let's recall the definition of cotangent in terms of sine and cosine: cot(x) = cos(x) / sin(x) We will use this definition to find the limit as x approaches π/4.Evaluating cosine and sine: Now, let's evaluate the cosine and sine of π/4: cos(π/4) = √2/2 sin(π/4) = √2/2 These are well-known values from the unit circle.Substituting values into cotangent expression: Next, we substitute these values into the cotangent expression: cot(π/4) = cos(π/4) / sin(π/4) = (√2/2) / (√2/2)Simplifying the expression: We simplify the expression by dividing the numerators and the denominators: cot(π/4) = (√2/2) / (√2/2) = 1Concluding the limit: Since the limit of cot(x) as x approaches π/4 is simply the value of cot(π/4), we conclude that: lim_(x → π/4) cot(x) = 1

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lim_(x rarr(pi)/(4))cot(x)=?
Choose 1 answer:
(A)
(sqrt2)/(2)
(B) 1
(C)
sqrt2
(D) The limit doesn't exist.

$\lim _{x \rightarrow \frac{\pi}{4}} \cot (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{\sqrt{2}}{2}$ $\newline$ (B) $1$ $\newline$ (C) $\sqrt{2}$ $\newline$ (D) The limit doesn't exist.

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\lim _{x \rightarrow \frac{\pi}{4}} \cot (x)=?

\newline

Choose

1

answer:

\newline

(A)

\frac{\sqrt{2}}{2}

\newline

(B)

1

\newline

(C)

\sqrt{2}

\newline

(D) The limit doesn't exist.

Recalling the 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 will use this definition to find the limit as $x$ approaches $\frac{\pi}{4}$ .
Evaluating cosine and sine: Now, let's evaluate the cosine and sine of $\frac{\pi}{4}$ : $\newline$ $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ $\newline$ $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ $\newline$ These are well-known values from the unit circle.
Substituting values into cotangent expression: Next, we substitute these values into the cotangent expression: $\cot(\pi/4) = \frac{\cos(\pi/4)}{\sin(\pi/4)} = \frac{\sqrt{2}/2}{\sqrt{2}/2}$
Simplifying the expression: We simplify the expression by dividing the numerators and the denominators: $\cot(\frac{\pi}{4}) = \frac{\sqrt{2}/2}{\sqrt{2}/2} = 1$
Concluding the limit: Since the limit of $\cot(x)$ as $x$ approaches $\frac{\pi}{4}$ is simply the value of $\cot\left(\frac{\pi}{4}\right)$ , we conclude that: $\newline$ $\lim_{x \to \frac{\pi}{4}} \cot(x) = 1$