Consider the function f(x) coefficients. (a) do (b) a6 (c) ag (d) b7 (e) bg = 8 + 5 sin²(4x) restricted to the interval [-л,л]. Calculate the following Fourier

write sin(3x)cos(6x) + cos(3x)sin(6x) as a single trig function

S sec²x(2cosx + sinx)²dx

A cable hangs between two poles of equal height and 26 feet apart. Set up a coordinate system where the poles are 13, where x is measured in feet. The height (in feet) of the cable at position x is placed at x = -13 and x = h(x) = 18 cosh(x/18), where cosh(x) = (eª + e¯*)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is feet long.

Identify the outside and inside functions for each of these composite functions. (a) y = √(4x + 9x2)          (c) y = sec5 x                                                               (b) y = tan(x 2 + 1)           ( d) y = ( 1 + ex)4

Find the number of roots of the function f(x) = 1 (x+1)³ --3x+sinx.

Find a0 of the function f(x) = sin(x/2)

Separate tanh-1(x+ iy) into real and imaginary parts.

Consider 3 4+2³ (a) First, define this as a Mathematica expression and compute the third derivative. (b) Now use Part (a) to compute the third derivative at z = 2. (c) Next, define it as a Mathematica function and compute the third derivative. (d) Now use the function to compute the third derivative at a = 2.

] B2(a): Find the derivative of the function 10x + 4 Y : and simplify the answer: 5а — 4 -