b) Let f [-T, π] → R be the function defined by N=∞ f (2) = Σ sin(nx) sin(x) sin(2x) sin(3x) + + +... 2n 2 4 8 n=1 Evaluate ƒ ƒ²(x) dx and ſ™ f(x) sin(3x) dx -π

1. Use the Fundamental Theorem of Calculus,, to find each derivative: (a) (b) (c) d 13 √ √9-y² dy dx d dx Jo d 3 tan x 9 + y² 2y + 1 3x³ #C+04 (1 + t) dy √2√x dx dy

8. Consider the functions f : (4, 0) → R where f(x) = sin x and g : (-12,3) → R where g(x) = |x + 5|. %3D (a) Find the rule for the function f o g. (b) Find the domain for the function f o g.

Consider the function f(x) = 6x + 12 sin x on the domain [0, 2π]. Use analytic techniques (calculus, algebra, trigonometry) to determine the intervals where the function is increasing and decreasing. Use exact values in your response. f(x) is increasing on f(x) is decreasing on