Using L’Hôpital’S Rule To Solve The Limit Of (1-Cosx)/X As X Approaches 0

lim x->0 1-cosx/x

0

To solve this limit, we can use L’Hôpital’s rule, which states that if the limit of f(x)/g(x) as x approaches some value results in a 0/0 or ∞/∞ indeterminate form, then we can take the derivative of both the numerator and denominator and re-evaluate the limit. We can keep applying L’Hôpital’s rule until the indeterminate form is resolved.

In this case, we have:

lim x->0 (1-cosx)/x

Since this is a 0/0 indeterminate form, we can use L’Hôpital’s rule and find the derivative of the numerator and denominator:

lim x->0 -sinx/1

The derivative of 1 is 0, so we are left with:

lim x->0 -sinx

Evaluating this limit, we get:

– sin(0) = 0

Therefore, the limit of (1-cosx)/x as x approaches 0 is 0.

In summary, the answer is:

lim x->0 (1-cosx)/x = 0

More Answers: