Define a function y = P(x) that represents the "period" of g(x)=sin(f(x)) or h(x) = cos(f(x)) provided that f is a continuous non-linear function. (The period is the interval of x-values over which sin(f(x)) or cos(f(x)) varies through one full cycle of values).  Under what conditions is P(x) an increasing function? Under what conditions is P(x) decreasing? Define f so that P(x) is a non-constant linear function of x.

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

A:

Q: Show that the functions f and g are identically equal.

A: Given functions are -  f(x) = sin x . tan x g(x) = sec x - cos x We have to show that f and g both…

Q: what is a function that takes the same value as im(z) on  γ(0;1)

A: We are to find out the function that takes the same value as im(z) on γ(0;1)   There are many…

Q: The function f is periodic (5 Puan) f (x) = sin (sin x) %3D false true

A: True. The given function is periodic. Check the following graph of given function.

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

A:

Q: The derivative with respect to x of 2 cos (x² + 2) is A. 2 sin (x²+2) cos (x² + 2) -2 sin (x² + 2)…

A:

Q: 2. Suppose f(x+3)%3D f(xr), what is the period of the function f ? (A) 4 (B) 3 (C) 2 (D) 1

A: topic - functions

Q: Find the intervals in which the function f(x)=sin (log,x)+cos(log,x)is decreasing.

A: By the first derivative test, a function is decreasing if its derivative is less than zero.

Q: The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high…

A: Given, Difference between low and high water level = 18 m  y = D + A cos (B(t - C))

Q: Differentiate the following functions w.r.t. x: (а) х* (b) cos (x*).

A: Using the product rule of differentiation, it can be written that f·g'=f '·g+f·g'. If c=ab , then,…

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: Sketch a graph of the function f(x) : – 2 sin(x + n). - 3- -Зл/2 -5л14 -3T|4 -T/2 -T/4 Зл14 5л14…

A: Graph of sine function

Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

A: