4 (3 points) Find the limit. (You should already memorize them.) (a) lim,-in() (b) lim-0 1-cos(a) (c) limo Problem (4a) (5 points) Using the (limit) definition of derivative to show that

the derivative of the function cosa is - sinx, i.e., cos x=- - sinz. [Hint: sin(a + 3) = sin a cos 3 + cos a sin 3. cos(a + 3) = cos a cos 3 sin a sin 3.] of the function cot(r) is csc²(r), i.e., Problem (4b) (5 points) Using the quotient rule of derivative to show that the derivative cot(x) = -csc² (r).