lim x->0 sinx =
To find the limit of sinx as x approaches 0, we can analyze the behavior of the sine function as x gets arbitrarily close to 0
To find the limit of sinx as x approaches 0, we can analyze the behavior of the sine function as x gets arbitrarily close to 0.
The sine function is defined as the ratio of the length of the side opposite to an angle in a right-angled triangle to the hypotenuse. However, we can also look at it from a more analytical viewpoint.
By the unit circle definition, on the unit circle, the angle formed by the positive x-axis and the radius to a point (x, y) is equal to the inverse sine of y. In other words, if we let the point (x, y) move along the unit circle, the y-coordinate of the point represents sin(theta), where theta is the angle formed.
Now let’s consider the values of sinx as x approaches 0 from both positive and negative sides. As x approaches 0 from the positive side (x > 0), the y-coordinate of the point on the unit circle moves closer and closer to 0, but never reaches 0 itself. Similarly, as x approaches 0 from the negative side (x < 0), the y-coordinate of the point on the unit circle moves closer and closer to 0, but still never reaches 0. From this observation, we can say that the limit of sinx as x approaches 0 does exist, and it is equal to 0: lim x->0 sinx = 0
More Answers:
Analyzing the Behavior and Finding the x-Value at Which Function g Attains a Relative MaximumAnalyzing the function f(x) = √(|x-2|) | True statement and graph analysis
Analyzing the Function f(x) = (x – 3)2 and Determining the Corresponding Graph