Chapter 4.1, Problem 1E

In Exercises 1-8, use the given substitution and the Chain Rule to find dy/dx. 1. y = sin (3x + 1), u = 3x + 1 2. y = sin (7 – 5x), u = 1- 5x 3. y = cos (V3r), u = V3r 4. y = tan (2x – x), u = 2x – x sin x sin x 5. у 1+ cos x 1+ cos x 2 6. у 5 сot 2 7. y = cos (sin x), u = sin x A 8. y = sec (tan x), u = tạn x can

2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

3 1-x 2.Find , *(x³ + y)dydx

1. Evaluate sec2 x dx (a) o Ta(x+ 4) dx (b) 1- tan² x

•2 x+1 2) Evaluate J1 T3x-2 dx using the substitution u = 3x – 2 3) Evaluate f2 e* cosx dx

Find S - Cosx (x² + 1)² elx

2. By hand, sketch the following against independent variable t: a) x₁(t) = Re(2e(-1+j2m)t) b) x₂ (t) - Im(3-e(1-j2n)t) 3. Find and sketch the odd and the even components of the following: a) tu(t) b) Sin(wot)u(t)

-5 -4 -3 -2 -1 9\10 11 12 13 14 15 a) f(4x)dx f (8 sin x) e) [F(4x - 1)dx csc(3x)f(6csc(3x))cot(3x)dx d) sec x

Need only a handwritten solution only (not a typed one).