Take home

#2 Hint:

#3 Hint:

You can use this trig identity

#5 Hint:

Consider , where g and h are the position functions of the two runners.

#6 Hint:

#7 Hint:

Induction would be much much harder than L'Hopital.

#8 (b)Hint:

Use

#8 (d)Hint:

Divide the square root of x in to each number in the numerator to make it easier to see what the anti derivative should be.

#9 Hint:

Draw a diagram look at the triangles.