23: The type is
∞⋅0.
Here is is not immediately clear what is the better
choice for "putting under". In both options we get a complicated composed
function in the denominator, so there is no difference there. Thus it may
help to look at the numerator. If we leave the tangent there, then after
differentiating it we get cosine to power negative two, which is troublesome
at point 1. On the other hand, if we leave the logarithm in the numerator,
derivative will turn it into 1/x, which is nice at 1. Thus the better
choice is to "put under" the tangent.
Answer