How do you find the limit of tantheta/theta as theta->0?

1 Answer
Nov 2, 2016

L'Hôpital's rule applies. Please see the explanation.

Explanation:

Because the expression evaluated at the limit is an indeterminate form, 0/0, L'Hôpital's rule applies.

Take the derivative of the numerator

(d[tan(theta)])/(d theta) = sec^2(theta)

Take the derivative of the denominator

(d theta)/(d theta) = 1

Assemble this into a fraction with the same limit:

lim_(thetato0)(sec^2(theta))/1 = sec^2(0)= 1

According to L'Hôpital's rule, the original expression goes to the same limit:

lim_(thetato0)(tan(theta))/theta = 1