Question

find the limit of the function algebraically.
lim
x->0

(2sinx)/(8x)

Answer 1

This would give you 0/0 thus you have to use L'Hospital's (L'H) rule to solve

lim (2sinx)/(8x) = lim 2cos(x)/8 = 2/8 = 1/4
x->0 L'H x-> 0

To use L'Hospital's rule you take the derivative of the numerator separately
Then you take the derivative of the denominator separately. Then you see if you can plug in the limit if you cannot apply L'H rule until you can.

This cannot be done algebraically, are you sure you didn't make a mistake writing the question?