Compute
limx→∞ 1 x 2 sin 1 x 2 . Hint: sine should suggest a certain
approach.

Compute limx→∞ 1 x 2 sin 1 x 2 . Hint: sine should suggest a certain...
1. Express function Faz) = sin(A sin tr), 0 < x < as a Fourier sine series. λ is a parameter. Hint: use the integral representation for Bessel functions.
evaluate using l'Hospital's rule limx→∞ (4+1/x)^-2/x
2. Prove that 4 a. limx→1 4 b. lim,→1 x-1 2
Evaluate limx---5- Evaluate limx ns (o take a (x2+2x+1)|x+51 (x+3)(2x+10)
(d) Compute 2m f(x) sin(3cr)d (Hint: Recall that sin2(2nnx/a)dx = f 2(2nnx/a)dx = £] COS'
(d) Compute 2m f(x) sin(3cr)d (Hint: Recall that sin2(2nnx/a)dx = f 2(2nnx/a)dx = £] COS'
4.1.26 If y has the double sine series Ek by sin kx sin ly, show that Poisson's equation - Uxx - Wyſ is solved by the double sine series u = b sin kx sin ly/(k? + 1). This is solution with u = 0 on the boundary of the square -1 < x, y <n.
fourier analysis
2. (a) Find the Fourier sine transform of b) Write f(x) as an inverse sine transform Hint: Don't directly calculate F,[f (x)(w). Begin with showing the representation sin wxdw. x >0 ㄧㄨ and then interchanging x and w in the representation. Now look at it carefully, what does the equation tell you?
Practice: Plot x vs y when y sin(x), y cosx), y sin (2"x), and y-2 sin(x) when x-1:0.1:10. Use 2 by 2 subplot, sin(x) is in location 1, cos(x) is in location 2, sin(2x) is in location 3 and 2 sin(x) is in location 4 The plot should have: (1) x labe|-"х value", y label = 'y value', legend 'y=sin(x)',' y-cos(x)',' y-sin (2*x)', "y-y-2*sin(x), and title = "X Vs. y, under Font Name of Times New Roman, and Font Size...
need help with these two. thank you.
Compute sine of the angle A= arcsin(-6/14)+arcos(-6/10). Given sin 6x-sin 6x=0 Find the solution that corresponds to the positive k=1 solution for the cosine part.
The sine function f(x)=sin(x) has a peak for values of , where n=1,5,9... List the first 5 values of x for which the sine function has a peak