Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→1 1 − x + ln(x) 1 + cos(5πx)

Evaluating the limand directly at gives an indeterminate form . Apply L'Hospital's rule once and we get

Again, plugging in returns . Apply the rule once more:

Now, in the denominator, when we get , so the limit is .

1/800 is the right answer