calculates the value of the following limit.

Solution

Now, notice that if we plug in θ =0 which we will get division by zero & so the function doesn't present at this point. In fact, we get 0/0 at this point, but due to the division by zero this function does not exist at θ =0.

Get table of values

It looks like the function is moving in towards a value of zero as θ moves in towards 0, from both of the sides of course.

Thus, the we will guess that the limit has the value,

So, once again, the limit had a value even though the function didn't exist at the point we were interested in.