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}
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) ?
If u(t) = < sin(8t), cos(4t), t > and v(t) = < t,
cos(4t), sin(8t) >, use the formula below to find the given
derivative.
d/(dt)[u(t)* v(t)] =
u'(t)* v(t) +
u(t)* v'(t)
d/(dt)[u(t) x v(t)] =
<.______ , _________ , _______>
If u(t) = < sin(5t),
cos(5t), t > and
v(t) = < t, cos(5t),
sin(5t) >, use the formula below to find the given
derivative.
d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)
d/dt [ u(t) x v(t)] = ?
a) Calculate and plot the DTFT of ?[?] = sin( (?/ 4)?) / ?? *
cos ( ?/2 ?) by hand.
b) By using a 2x1 subplot, plot ?[?] signal defined in Question
1 in the first row. Take ? between -100 s and 100 s and limit
x-axis between -20 sand 20 s. Be careful about when ? = 0. What is
the value of ?[0]? While plotting ?[?] please write an if statement
for ? = 0. After...
Show
that in 2D, the general orthogonal transformation as matrix A given
by
{{cos, sin}, {-sin, cos}}. Verify that det[A] = 1 and that the
transpose of A equals its inverse. Let Tij be a tensor in this
space. Write down in full the transformation equations for all its
components and deduce that Tii is an invariant.
Question 1
a. cos Ѳ =-24/25, Ѳ in quadrant 3, find sin Ѳ
b. sin Ѳ=12/13, Ѳ in quadrant 2, find cos Ѳ
c.cos Ѳ =12/13,270 degrees<Ѳ <360 degrees, find sin Ѳ
d.find the reference angle for 279 degrees