a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l
sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y)
+-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is
given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the
numeric value for the AM index of modulation, m, fors(f) ?
Find dy/dx for a & b
a) sin x+cos y=1
b) cos x^2 = xe^y
c)Let f(x) = 5 /2 x^2 − e^x . Find the value of x for which the
second derivative f'' (x) equals zero.
d) For what value of the constant c is the function f continuous
on (−∞,∞)?
f(x) = {cx^2 + 2x, x < 2 ,
2x + 4, x ≥ 2}
Consider the function given as example in lecture: f(x, y) = (e
x cos(y), ex sin(y)) (6.2) Denote a = (0, π/3) and b = f(a). Let f
−1 be a continuous inverse of f defined in a neighborhood of b.
Find an explicit formula for f −1 and compute Df−1 (b). Compare
this with the derivative formula given by the Inverse Function
Theorem.
How does the graph of y = sin x compare with the graph of y = cos x? Explain how you could horizontally translate the graph of y = sin x to obtain y = cos x.