lim_(x rarr(pi)/(6))sin(x)=? Choose 1 answer: (A) (1)/(2) (B) (sqrt2)/(2) (c) sqrt2 (D) The limit doesn't exist.

Direct Substitution: To find the limit of sin(x) as x approaches π/6, we can directly substitute x with π/6 in the function sin(x), because sine is a continuous function and we can evaluate the limit by direct substitution. Substitute x: Substituting x with π/6 in sin(x), we get sin(π/6). Trigonometric Identities: The value of sin(π/6) is known from trigonometric identities, which is 1/2. Final Limit: Therefore, the limit of sin(x) as x approaches π/6 is 1/2.

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lim_(x rarr(pi)/(6))sin(x)=?
Choose 1 answer:
(A)
(1)/(2)
(B)
(sqrt2)/(2)
(c)
sqrt2
(D) The limit doesn't exist.

$\lim _{x \rightarrow \frac{\pi}{6}} \sin (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2}$ $\newline$ (B) $\frac{\sqrt{2}}{2}$ $\newline$ (C) $\sqrt{2}$ $\newline$ (D) The limit doesn't exist.

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

Full solution

\lim _{x \rightarrow \frac{\pi}{6}} \sin (x)=?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2}

\newline

(B)

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

\newline

(C)

\sqrt{2}

\newline

(D) The limit doesn't exist.

Direct Substitution: To find the limit of $\sin(x)$ as $x$ approaches $\frac{\pi}{6}$ , we can directly substitute $x$ with $\frac{\pi}{6}$ in the function $\sin(x)$ , because sine is a continuous function and we can evaluate the limit by direct substitution.
Substitute $x$ : Substituting $x$ with $\frac{\pi}{6}$ in $\sin(x)$ , we get $\sin\left(\frac{\pi}{6}\right)$ .
Trigonometric Identities: The value of $\sin(\frac{\pi}{6})$ is known from trigonometric identities, which is $\frac{1}{2}$ .
Final Limit: Therefore, the limit of $\sin(x)$ as $x$ approaches $\frac{\pi}{6}$ is $\frac{1}{2}$ .