## lim x->0 1-cosx/x

### To evaluate the limit of the given expression as x approaches 0, we can use the limit properties and some trigonometric identities

To evaluate the limit of the given expression as x approaches 0, we can use the limit properties and some trigonometric identities.

The given expression is:

lim x->0 (1 – cos(x))/x

To simplify this expression, we can use the fact that cos(0) = 1. So, we can substitute cos(0) into the expression:

lim x->0 (1 – cos(0))/x

This simplifies to:

lim x->0 (1 – 1)/x

lim x->0 (0)/x

Since we have 0 divided by any value of x, the limit of the expression as x approaches 0 does not exist because we have an indeterminate form, 0/0.

Alternatively, we can use L’Hôpital’s Rule to evaluate this limit. L’Hôpital’s Rule states that if we have a limit of the form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator until the limit becomes determinate.

Taking the derivative of the numerator and denominator:

lim x->0 (1 – cos(x))/x = lim x->0 (-sin(x))/1 = -sin(0) = 0

Therefore, using L’Hôpital’s Rule, we find that the limit of the expression as x approaches 0 is 0.

In conclusion, the limit of (1 – cos(x))/x as x approaches 0 is either undefined (indeterminate form) or equal to 0 depending on the method used.

## More Answers:

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