The question is not correctly visible. but I have solved it. I
hope the assumed equation by me is correct. I f wrong assumption by
me then comment it, I will solve accordingly.
f(x,y)=sin(2x)sin(y)
intervals for x and y:
-π/2 ≤ x ≤ π/2 and -π ≤ y ≤ π
find extrema and saddle points
In the solution, I mainly interested how to
findcritical points in case of the system of trigonometric
equations (fx=0 and fy=0).
,
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) ?
Solve the initial value problem dy/dx = −(2x cos(x^2))y +
6(x^2)e^(− sin(x^2)) , y(0) = −5
Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1
+ t^6)^2 , y(1) = 8.
Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
Write a program (fortran 90) that calls a subroutine to
approximate the derivative of y=sin(x)+2x^2 using a one-sided
difference approach fx = (fi-fi-1)/deltaX and a centered difference
approach fx = (fi+1-fi-1)/deltaX. The value of the function f and
its derivative fx should be evaluated at x=3.75. Your code should
print both values tot he screen when it runs.
Let f ( x , y ) = x^ 2 + y ^3 + sin ( x ^2 + y ^3 ). Determine
the line integral of f ( x , y ) with respect to arc length over
the unit circle centered at the origin (0, 0).