Question

How do you find `lim (1-cosx)/x` as `x->0` using l'Hospital's Rule?

Answer 1

`0`

Explanation:

Note that we're in indeterminate form (`0/0`), so we can use l'Hospital's Rule.

L'hospital's Rule states that `lim_(x->c) (g(x))/(h(x)) = lim_(x->c) (g'(x))/(h'(x))`.

Therefore:

`lim_(x->0) (1- cosx)/x`

`=lim_(x->0) ((1 - cosx)')/(x')`

`=lim_(x->0) (sinx)/1`

`=sin(0)/1`

`= 0`

Hopefully this helps!