-4 m 1.0 1,0 0 Let f(x) = {º (3 - x) • - - -3 for 0 < x < 1, for 1 < x < 3. Compute the Fourier sine coefficients for f(x). • Bn

Let f′′(θ)=sin(θ)+cos(θ) and suppose that f(0)=6 and f′(0)=10.  What is the sum of the coefficients on all 4 terms in f(θ)?

Compute the derivative of the given function. sin ¹(x³ + 4) O O O d -[sin ¹(x³ + 4)] = dx d dx d dx d dx √ + 1-(-³ 4) 2 (x³ + 4) [sin ¹(x³ + 4)] = √/1 + (x² + 4)² (3x+²) +4)2 [sin¯¹(x³ + 4)] = = -[sin¯¹(x^³ + 4)] = 3x² 1 - (x³ + 4)² 1 1 – (x-³. (3x-²) +4)²

[eax sin(bx)] dx = 1 eax[a sin(bx) – b cos(bx)] + C ах * Using the formula \a² + b², le-8* sin(6x)] dx Evaluate

The trigonometric substitution x - 2 = 3 sec 0 could be useful in integrating a function (i.e., an integrand) involving... (a) √x² 4x + 5 (b) x² 4x - 5 (c) 9 - (x - 2)² (a) √ (x - 2)² +9 (e) 4x9

Let z be a complex number.

(1 point) Approximate cos(4.6) using a quadratic approximation: First note that cos(4.6) cos(3/2). Let f(x) = cos(x). Then, f'(x) = -sinx and f"(x) = -cosx Let a = 3x/2. Then f' (3/2) = -sin(3pi/2) and f" (3л/2) = -cos(3pi/2) Q(x), the quadratic approximation to cos(x) at a = 3/2 is: Q(x) = cos(3pi/2) Use Q(x) to approximate cos(4.6). cos(4.6) cos(3pi/2)

(max, argmax, min, argmin) Let f(x) := (2+ sin(27x)) and A := [0, 2]. Compute: max,A f(x) and argmax f(x). XEA EA Compute: min, f(x) and argmin f(x). Compute: argmax 2 - eM9+5 _ 7]. Compute: argmin [11 – In (2 · f(x) + 5)].

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