a) Evaluate lim(x-->infinity) ln(x^50)/x^100. Please reference any theorems and examples that you used to answer this question.
b) A hiker leaves his cabin at 7:00am and takes his usual path to the top of the mountain, arriving at 7:00pm.The following morning he starts at 7:00am at the top and takes the same path back ,arriving at his cabin at 7:00pm. USE THE INTERMEDIATE VALUE THEOREM to explain that their is point on the path that the hiker will cross exactly at the same time of day at both days.