-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

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

PART D ONLY PLEASE

verify sin2(x)+cos2(x)=1

Find the first derivative of y = Arc tan √√x² − 1 + Arc csc x 2 O O 0 X . Find the first derivative of y = sin² (7x + 1) 2 In 7 sin(7* + 1) cos(7* + 1) O-2 In 7 sin (7* + 1) cos(7* + 1) 2 In 7 sin(7* + 1) cos(7* + 1)7* In 7 sin(7* + 1) cos(7* + 1)

Evaluate the function 1+ 2e + 3e2t + 4e3t at t = 1 by using 3 digit rounding and (a) The form exactly as it is shown. (b) Horner's method (considering = e'). Which method is more accurate?

Solve for Fourier coefficient, Ssin x 02x27 f(x)= 0 T >x 22n cosx sec x + cosx csc csc² x csc? x secx cos? x cos x cos x § f(x)dx _ ? If f(x)* , then 1

Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

Find the derivative of the following a) y = cos (4x³ + x²-2) -1 b) y = xsin ¹¹ (x) + √√√1-x²