Chapter 4.1, Problem 3E

Q2/ 1. If y = cos(2t + 5) find using chain rule

S.S (sin x + cos y)e dx dy dz A. 2n(e2n + e3) B. 2m(e2 – e3") c. 2m(e + e2") D. 2n(e – e2™)

მა A. Use the chain rule to find Ət = მა Suppose z = = B. Find the numerical values of (-5, -2) (-5,-2): x² sin y, x = 3s² - 2t² y = = = = and Ət and 18 10st. as functions of x, y, s and t. when (s, t) = (-5, -2).

A graph of f (z) =a cos(br) is shown, where b is a positive constant. |(0, 4) (T, 4) |(27, 4) -2 (T/2, -4) (Зл/2, -4) Determine the values of a and b. O a = 4; b = 2 O a = 8; b = 2 O a = 4; b = 4 O a = 8; b= 4

determine the d.e.

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

Consider h(t) = | e e-3 3(t-T) cos(27)dr. This is the convolution of two functions f(t) and g(t). That is, h(t) = (g * f)(t). Identify the two functions: f(t) = g(t) =

Verify directly that the relation y = C, e* cos bx + c, e* sin bx satisfies the equation [(D – a)? + b²]y = 0.

Differentiate. H(t) = cos2(t)