Let f(x) = sin(x) for -pi < x < pi and be ZERO outside
this interval...
Let f(x) = sin(x) for -pi < x < pi and be ZERO outside
this interval
a. Find the Fourier Transformation. Plot on Desmos.
b. Find the Fourier Integral representation of f(x). Plot on Desmos
using
reasonable limits of integration
S(x) is a cubic spline for the function f(x) = sin(pi x/2) +
cos(pi x/2) at the nodes x0 = 0 ,
x1 = 1 , x2 = 2
and satisfies the clamped boundary conditions. Determine the
coefficient of x3 in S(x) on [0,1] ans. pi/2 -3/2
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).
Consider the function on the interval (0, 2π).
f(x) = sin(x) cos(x) + 2
(a) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
( )
decreasing
( )
(b) Apply the First Derivative Test to identify all relative
extrema.
relative maxima
(x, y) =
(smaller x-value)
(x, y) =
( )
(larger x-value)
relative minima
(x, y) =
(smaller x-value)
(x, y) =
...
Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2
+ (cos(x))^2 (a) Find the open intervals on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) increasing decreasing (b) Apply the First Derivative
Test to identify the relative extrema. relative maximum (x, y) =
relative minimum (x, y) =
Find the absolute max and min of f(x)= e^-x sin(x) on the
interval [0, 2pi]
Find the absolute max and min of f(x)= (x^2) / (x^3 +1) when x
is greater or equal to 0