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

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Understanding the tangent function: To solve the limit of tan(x) as x approaches 0, we need to understand the behavior of the tangent function near 0. The tangent function is defined as the ratio of the sine function to the cosine function, so we can express tan(x) as sin(x)/cos(x).Applying limit properties: We know that the limit of sin(x) as x approaches 0 is 0, and the limit of cos(x) as x approaches 0 is 1. This is a direct application of the limit properties of trigonometric functions.Dividing the limits: Using the limit properties, we can divide the limits of the numerator and the denominator as long as the limit of the denominator is not 0. Since cos(0) = 1, we can safely divide the limits.Calculating the limit of tan(x): Now we calculate the limit of tan(x) as x approaches 0 by dividing the limits of sin(x) and cos(x): lim_(x -> 0) tan(x) = lim_(x -> 0) (sin(x)/cos(x)) = (lim_(x -> 0) sin(x)) / (lim_(x -> 0) cos(x)) = 0 / 1 = 0.Conclusion: Therefore, the limit of tan(x) as x approaches 0 is 0, which corresponds to option (B).

$\lim _{x \rightarrow 0} \tan (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $-1$ $\newline$ (B) $0$ $\newline$ (C) $1$ $\newline$ (D) The limit doesn't exist.

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$\lim _{x \rightarrow 0} \tan (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $-1$ $\newline$ (B) $0$ $\newline$ (C) $1$ $\newline$ (D) The limit doesn't exist.