limit as x approaches 0: 1-cosx/x
To find the limit as x approaches 0 of the expression (1 – cos(x))/x, we can use L’Hôpital’s Rule or the properties of trigonometric limits
To find the limit as x approaches 0 of the expression (1 – cos(x))/x, we can use L’Hôpital’s Rule or the properties of trigonometric limits.
Let’s start with L’Hôpital’s Rule:
Taking the derivative of the numerator (1 – cos(x)), we get 0 + sin(x) = sin(x).
Taking the derivative of the denominator (x), we get 1.
Now, we can rewrite the expression as the limit of sin(x)/x as x approaches 0.
Using the trigonometric limit property, we know that the limit of sin(x)/x as x approaches 0 is 1. Therefore, the limit of (1 – cos(x))/x as x approaches 0 is also 1.
In conclusion, the limit of (1 – cos(x))/x as x approaches 0 is 1.
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