Approaching the Limit: The Continuity of sin(x) as x Goes to 0

lim x->0 sinx =

To find the limit of sin(x) as x approaches 0, we can use the concept of continuity and the value of the sine function for small angles

To find the limit of sin(x) as x approaches 0, we can use the concept of continuity and the value of the sine function for small angles.

The sine function is defined as the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. As the angle approaches 0, the triangle becomes very small, and the length of the side opposite the angle approaches 0 as well.

Therefore, as x approaches 0, sin(x) approaches 0. In mathematical notation, we can express this as:

lim(x→0) sin(x) = 0

More Answers:

The Intermediate Value Theorem: Exploring the Existence of Solutions for Continuous Functions on Closed Intervals
The Extreme Value Theorem: Ensuring the Existence of Maximum and Minimum Values for Continuous Functions on Closed and Bounded Intervals
Using the Squeeze Theorem to Evaluate Limits in Calculus

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