The following periodic function f(t) of period 27 is specified over one period -π ≤ t ≤ π: 0 when -π≤ t ≤ - T -9 cos(t) when −

2. Let f(x) = 3 cos(2x) – 1. (a) Find the period and the amplitude. (b) Sketch the graph of the function f (x) in [0, 2n) by using 5 key points.

Given the graph of the function f(x) = = O k|m 3TT K|N 02/12 О п -TT TT/2 50 4 3 2 -1- P -1- -2 -3 -4 -5 TT/2 E- TT 3TT/2 tan (2x) above, determine the period of the graph. EN

The following represents the graph of the function: OS(x) = cos x- cos x+- 2 2 X. TU2 3 T/ 2 (points) Based on the graph of this function do the following: a. Use your understanding of how to identify the parameters of the sinusoidal function y = asin(hx +c) + d or y = acos(hx +c)+d_to write the equation of a simpler function p(x) that describes the graph. Explain your choices. b. Check the answer you obtained in (a) by graphing the new function p(x). Obtain a printout of the graph. Explain how you used your graphing calculator to verify that your answer is сопеct. c. Verify algebraically that the two equations are equivalent.

6. Sketch the graph of the function over one period y 2+ sin(4x). Plot at least three points exactly.

State the amplitude and period of the function f: R → R, ƒ (x) = 3 – 6cos (**-) а. b. Find the general solution of 3 – 6 cos (*) = 0 Sketch the graph of the function f:[0,8] → R, f (x) = 3 – 6cos () below, clearly stating the coordinates of all axial intercepts, end points and turning points. с. on the axes 16 17 ORMITUniversity

The function f(x)= sec(x) is periodic with period 2π

Compute the first and second derivatives of the functions: 1.) 2.) 3.) y=tan(x/3) y=sin(0.5√√x)/x y=e* + x at x = 3 at x = 1 at x=2

Part of the graph of the periodic function f is shown below. The domain of f is 0 sxs 15 and the period is 3. 9. Ax), 3- 2+ 1. 7 8. 10 (a) Find (i) f(2); (ii) f' (6.5); (iii) f' (14). (b) How many solutions are there to the equationf(x)=1 over the given domain? 4. 3.

find root of f(n) = 3X + Sin (x) - e²? fig 5 shows the (x) = 3X + Sin (x) - ex. It's clear form the graph that there are two Poots, one lies between 0 and 0.5 and the other between 1.5 and 2.0. Consider the function F(x) in the interval [0, 0.5] Since f(0) * f(0.5) less than Zero. X f 0 0.5 -2 Fig. 5 1.5