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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 funct...
Question 8 a) Sketch the graph of y=sin(x) and y=sin(2x) for 0<xs. b) Show that the...
Question 8 a) Sketch the graph of y=sin(x) and y=sin(2x) for 0<xs. b) Show that the area of the region bounded by these graphs is 4
Find the amplitude, period, and phase shift of the function. y = 2 sin(x - 1)...
Find the amplitude, period, and phase shift of the function. y = 2 sin(x - 1) amplitude period phase shift Graph one complete period. у 1 V 2x 2x -2 0-31 31 Graph one complete period. 2 2x 21 0-31 AN - 2
Question 3: (15 Marks) Find centroid for the region R, that lies outside r - 2 and inside r 3 + 3 sin 6 Hint: Sketch gr...
Question 3: (15 Marks) Find centroid for the region R, that lies outside r - 2 and inside r 3 + 3 sin 6 Hint: Sketch graph in the range of 0e e <2T
Question 3: (15 Marks) Find centroid for the region R, that lies outside r - 2 and inside r 3 + 3 sin 6 Hint: Sketch graph in the range of 0e e
11. For parts (a-c) consider the polynomial function(x) = -2x²(x - 4)'(x - 1)*(x + 2)....
11. For parts (a-c) consider the polynomial function(x) = -2x²(x - 4)'(x - 1)*(x + 2). [10 Points) (a) What is the degree of the polynomial function? (b) List the zeros of the function in the table provided below and state the multiplicity of each zero. Describe the behavior of the graph at each of the zeros. Does the graph Touch/Cross at each zero? Zero Multiplicity Touch/Cross of 2 -6 -4 -2 -21 (c) Provide a rough sketch of the...
Use the steps below to sketch the graph y = x^2 - 7x - 18. Required...
Use the steps below to sketch the graph y = x^2 - 7x - 18. Required points are the x intercepts and the max and mix of the graph 1. Determine the domain of f. 2. Find the x- and y-intercepts of f.† 3. Determine the behavior of f for large absolute values of x. 4. Find all horizontal and vertical asymptotes of the graph of f. 5. Determine the intervals where f is increasing and where f is decreasing....
Given: Graph below - 120 60 30 30 60 90 120 150 180 210 240 270...
Given: Graph below - 120 60 30 30 60 90 120 150 180 210 240 270 300 330 360 390 1. State: domain and range x and y intercepts max and min values and where they occur period amplitude axis of symmetry values of a, k, d, and c for the sine function 2. Describe how this graph is related to the base function y=sin x by referring to horizontal and vertical shifts, amplitude, compressions or expansions, reflection.
Question 2 The function r) is defined by 3(x + 1) 1 f12r + 71-4 1+4...
Question 2 The function r) is defined by 3(x + 1) 1 f12r + 71-4 1+4 () (111) 13 marks Show that f(x)= [4 marks) Find (3) Find the domain off- [2 marks] Given that g(x) = In(x + 1) Find the solution of r if fg(x) = 5, by leaving your answer in terms of e exponential function) [4 marks) (b) Sketch the graph of the function, In)-1-cosx). not by plotting points, but starting with the graph of a...
4. Continuing with problem 3, f(x) = 2x? + 8x + 5. a) Find the x...
4. Continuing with problem 3, f(x) = 2x? + 8x + 5. a) Find the x and y intercepts. b) Give the domain of the function. c) Give the range of the function. d) Sketch the graph of the function.
4. Consider the periodic function given below: f(x)-x 0 ㄨㄑㄧ (i) State its fundamental period, and...
4. Consider the periodic function given below: f(x)-x 0 ㄨㄑㄧ (i) State its fundamental period, and sketch the function for 3 periods. (5 marks) i) Find the Fourier series of the given periodic function, and expand the series to give the first three non-zero a and b terms (15 marks) ii) Use the answer obtained in Q4(ii) and the given periodic function, find the sum of the series 4(2n-1 )2 (5 marks)
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
Question 8 a) Sketch the graph of y=sin(x) and y=sin(2x) for 0<xs. b) Show that the area of the region bounded by these graphs is 4
Find the amplitude, period, and phase shift of the function. y = 2 sin(x - 1) amplitude period phase shift Graph one complete period. у 1 V 2x 2x -2 0-31 31 Graph one complete period. 2 2x 21 0-31 AN - 2
Question 3: (15 Marks) Find centroid for the region R, that lies outside r - 2 and inside r 3 + 3 sin 6 Hint: Sketch graph in the range of 0e e <2T
Question 3: (15 Marks) Find centroid for the region R, that lies outside r - 2 and inside r 3 + 3 sin 6 Hint: Sketch graph in the range of 0e e
11. For parts (a-c) consider the polynomial function(x) = -2x²(x - 4)'(x - 1)*(x + 2). [10 Points) (a) What is the degree of the polynomial function? (b) List the zeros of the function in the table provided below and state the multiplicity of each zero. Describe the behavior of the graph at each of the zeros. Does the graph Touch/Cross at each zero? Zero Multiplicity Touch/Cross of 2 -6 -4 -2 -21 (c) Provide a rough sketch of the...
Given: Graph below - 120 60 30 30 60 90 120 150 180 210 240 270 300 330 360 390 1. State: domain and range x and y intercepts max and min values and where they occur period amplitude axis of symmetry values of a, k, d, and c for the sine function 2. Describe how this graph is related to the base function y=sin x by referring to horizontal and vertical shifts, amplitude, compressions or expansions, reflection.
Question 2 The function r) is defined by 3(x + 1) 1 f12r + 71-4 1+4 () (111) 13 marks Show that f(x)= [4 marks) Find (3) Find the domain off- [2 marks] Given that g(x) = In(x + 1) Find the solution of r if fg(x) = 5, by leaving your answer in terms of e exponential function) [4 marks) (b) Sketch the graph of the function, In)-1-cosx). not by plotting points, but starting with the graph of a...
4. Continuing with problem 3, f(x) = 2x? + 8x + 5. a) Find the x and y intercepts. b) Give the domain of the function. c) Give the range of the function. d) Sketch the graph of the function.
4. Consider the periodic function given below: f(x)-x 0 ㄨㄑㄧ (i) State its fundamental period, and sketch the function for 3 periods. (5 marks) i) Find the Fourier series of the given periodic function, and expand the series to give the first three non-zero a and b terms (15 marks) ii) Use the answer obtained in Q4(ii) and the given periodic function, find the sum of the series 4(2n-1 )2 (5 marks)
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
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