lim_(x rarr(pi)/(4))csc(x)=? Choose 1 answer: (A) (sqrt2)/(2) (B) (sqrt3)/(2) (c) sqrt2 (D) The limit doesn't exist.

Reciprocal of sin(x): To find the limit of csc(x) as x approaches π/4, we first need to remember that csc(x) is the reciprocal of sin(x). Therefore, we need to find the value of sin(π/4) to determine the value of csc(π/4). Value of sin(π/4): The value of sin(π/4) is a well-known trigonometric value. Since sin(π/4) = √2/2, we can then find the value of csc(π/4) by taking the reciprocal of sin(π/4), which is 2/√2. Rationalizing the denominator: To simplify 2/√2, we can multiply the numerator and the denominator by √2 to rationalize the denominator. This gives us (2√2)/(√2 * √2) which simplifies to √2. Limit of csc(x) as x approaches π/4: Therefore, the limit of csc(x) as x approaches π/4 is √2. This corresponds to choice (C) in the given options.

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lim_(x rarr(pi)/(4))csc(x)=?
Choose 1 answer:
(A)
(sqrt2)/(2)
(B)
(sqrt3)/(2)
(c)
sqrt2
(D) The limit doesn't exist.

$\lim _{x \rightarrow \frac{\pi}{4}} \csc (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{\sqrt{2}}{2}$ $\newline$ (B) $\frac{\sqrt{3}}{2}$ $\newline$ (C) $\sqrt{2}$ $\newline$ (D) The limit doesn't exist.

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Algebra 2

Is (x, y) a solution to the system of equations?

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

\newline

Choose

1

answer:

\newline

(A)

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

\newline

(B)

\frac{\sqrt{3}}{2}

\newline

(C)

\sqrt{2}

\newline

(D) The limit doesn't exist.

Reciprocal of sin(x): To find the limit of $csc(x)$ as $x$ approaches $\frac{\pi}{4}$ , we first need to remember that $csc(x)$ is the reciprocal of $sin(x)$ . Therefore, we need to find the value of $sin(\frac{\pi}{4})$ to determine the value of $csc(\frac{\pi}{4})$ .
Value of $\sin(\frac{\pi}{4})$ : The value of $\sin(\frac{\pi}{4})$ is a well-known trigonometric value. Since $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ , we can then find the value of $\csc(\frac{\pi}{4})$ by taking the reciprocal of $\sin(\frac{\pi}{4})$ , which is $\frac{2}{\sqrt{2}}$ .
Rationalizing the denominator: To simplify $\frac{2}{\sqrt{2}}$ , we can multiply the numerator and the denominator by $\sqrt{2}$ to rationalize the denominator. This gives us $\frac{2\sqrt{2}}{\sqrt{2} \times \sqrt{2}}$ which simplifies to $\sqrt{2}$ .
Limit of $\csc(x)$ as $x$ approaches $\frac{\pi}{4}$ : Therefore, the limit of $\csc(x)$ as $x$ approaches $\frac{\pi}{4}$ is $\sqrt{2}$ . This corresponds to choice (C) in the given options.