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#2 Hint:

#3 Hint:

You can use this trig identity
$\sin x \cos x = \frac12 \sin 2x$

#5 Hint:

Consider $f(t) = g(t) - h(t)$ , where g and h are the position functions of the two runners.

#6 Hint:

$\frac{d}{dx} |x| = sgn x = \frac{x}{|x|}$

#7 Hint:

Induction would be much much harder than L'Hopital.

#8 (b)Hint:

Use $\int_a^b f(t)dt =-\int_b^a f(t)dt$

#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.