MH1810 Use intermediate value theorem and mean value theorem to show that the graphs of y = cos x and y = x + 2 intersect exactly once: Math take home test Home Work, NTU, Singapore

Questions 1,2,3 carry 2 marks each and question 4 carries 3
marks. Total 9 marks. Answer ALL questions.

1. Use intermediate value theorem and mean value theorem to show that
the graphs of y = cos x and y = x + 2 intersect exactly once.

2. A 2.6 m ladder is leaning against a wall when its base starts to slide
away. By the time the base is 2.4 m from the wall, the base is moving
away at the rate of 1 ms1 : At what rate is the angle  between the ladder and the ground changing at this moment?

3. Express the following as a deÖnite integral R 1 0 f (x) dx and Önd its exact value. (Express your answer in terms of )