4. π a. The graph of y = cos x can be obtained by translating the...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this function 4 sin (22-9 ) for-r (b) Solve y π to find the horizontal intercepts x (a-intercepts) of the function. (c) Find the values of x for-π π for which the maximum. and the x minimum values of the function occur...
Supposez1 =4 cos 3 +isin 3 andz2 =2 cos 6 +isin 6 . Computez1z2. (a) 8(cos?π?+isin?π?) 22 (b) 4(cos?4π?+isin?4π?) 66 (c) 2(cos?π?+isin?π?) 66 (d) cos(π)+isin(π) (e) 8(cos?π?+isin?π?) 66 17. Suppose z1 = 4 (cos (1) + i sin (5)) and z2 = 2 (cos () + i sin (7)). Compute z122. (a) 8(cos (7) + i sin (7)) (b) 4(cos (4) + i sin (*)) (c) 2(cos (7) + i sin ()) (d) cos(T) + i sin(TT) (e) 8(cos (7)...
Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. (Round your answers to four decimal places.) f(x) = cos(x), [0, π/2], 4 rectangles
2. LetA = 〈cos-, sin? and B = 〈cosi' sin, be two vectors on the x-y plane. Let -(cos-, sin π〉 3 4 be another non-zero vector on the x-y plane not collinear with A or B. Show that A × B =-B × C. If we could cancel B, as we could if these were real numbers, is it true that A =-C? [Show your work and conclusions on a separate sheet of paper] 2. LetA = 〈cos-, sin?...
can someone show me how to graph this please 2 Y- FLUSJL). Statele dumplitude dru perido. 3) y = sin(x + ). State the shift and whether it is right or left. 4) y = 2 cos(x-3). State the shift and whether it is left or right.
Let f(x) be the 27-periodic function which is defined by f(x)-cos(x/4) for-π < x < 1. π. (a) Draw the graph of y f(x) over the interval-3π < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: 16k2 1 16k2 1 (16k2 1)2 に1...
13) Find an equation of the tangent line to the curve y=sin(5x)+cos(8x) at the point (π/6,y(π/6)). what is the tangent line: 14) f(x)=4x^2cos(4x) what is the first and second derivatives and solve both for F(5) NOTE There should be four answers! 16) Suppose that f(x)=3x/(4−5x^)3 find an equation for the tangent line to the graph of f at x=2. the tangent line: y=
Evaluate the integral Z π 0 Z π x cos(y) y dy dx. Hint: Since cos(y) y doesn’t have an elementary antiderivative in y, the integral can only be evaluated by reversing the order of integration using Fubini’s theorem.
Q a cos 7x- cos 9x The graph with the equation y= is shown sin 7x + sin 9x in a [0,2x,x] by [-2.2.1] viewing rectangle. a. Describe the graph using another equation. b. Verify that the two equations are equivalent 22 a. Write another equation of the given graph y = tan x (Type an equation using x as the variable) b. To verify that the two equations are equal, start with the numerator of the right side and...
Graph y = 2cos x, y = 2 cos 4x, and y = -2 + 2 cos 4x on the same set of axes. Draw the set of axes with intervals of length. TT