Homework Answers
Quetion 5 graph is not clear
Q3 (5 Marks) Find the values of x and y such that {(x + yi) =(-1...
Q3 (5 Marks) Find the values of x and y such that {(x + yi) =(-1 + 71)2 04: (6 Marks) Let Z2 = 5 + 7j a) Find the modulus and the argument of Zz. b) Express 2, in polar form r cose + r sino ; Q5. Let f(x) = 6x2 - 2x - 3, part of the graph of funtion shown below. (1+1+2 Marks) (a) Draw the graph of y = 2 on the same axis. (b)...
Q5. Let f(x) = 6x2 - 2x - 3, part of the graph of funtion shown...
Q5. Let f(x) = 6x2 - 2x - 3, part of the graph of funtion shown below. (1+1+2 Marks) (a) Draw the graph of y = 2 on the same axis. (b) Use the graph to find (0) The values of of x when 6x2 - 2x - 3 = 2 Find the cordinate of the vertex (1) Find the equation of the axis of symetry.
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6...
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
(2 points) Here are several points on the complex plane: The red point represents the complex...
(2 points) Here are several points on the complex plane: The red point represents the complex number zı = and the blue point represents the complex number Z2 = The "modulus" of a complex number z = x+iy, written [z], is the distance of that number from the origin: z) = x2 + y2. Find the modulus of zi. |zıl = 61^(1/2) We can also write a complex number z in polar coordinates (r, 6). The angle is sometimes called...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, cen...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
how do I find the x intercepts in part b? 1. (20 marks, Sec. 1.3) Let...
how do I find the x intercepts in part b?
1. (20 marks, Sec. 1.3) Let f and g be linear functions with equations f(x) mi+b and g(r)mb (a) Is the composition f o g a linear function? If so, what is the slope and y-intercept of its graph? (bIs the product f g a linear function? If not, what type of function is it? What are the r-intercepts?
QUESTION 6 [10 marks] F or the circuit below, a) [5 marks] Fin d the current...
QUESTION
6
[10
marks]
F
or the circuit below,
a) [5 marks] Fin
d the current phasor
I
x
using superposition.
b) [3 marks] Verify your answer in part a) using nodal or mesh
analysis.
c) [2 marks] Gi
ven the frequency
!
=
2
!"#
/
!"#
,
write
the corresponding
values for elements
R, L, C, and
the
expressions for source
s
v
x
(t)
and
i
y
(t)
on the diagram below.
QUESTION 7 [10 marks] For...
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch the region. 5x2-2. f(x)--3x2 + 30 and g(x) marks) c) Evaluate the follow...
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch the region. 5x2-2. f(x)--3x2 + 30 and g(x) marks) c) Evaluate the following integrals. Give your answers to 2 decimal places. dac i) 2 (3+2 dx. (8 marks) [25 marks]
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch...
Q3 (5 Marks) Find the values of x and y such that {(x + yi) =(-1 + 71)2 04: (6 Marks) Let Z2 = 5 + 7j a) Find the modulus and the argument of Zz. b) Express 2, in polar form r cose + r sino ; Q5. Let f(x) = 6x2 - 2x - 3, part of the graph of funtion shown below. (1+1+2 Marks) (a) Draw the graph of y = 2 on the same axis. (b)...
Q5. Let f(x) = 6x2 - 2x - 3, part of the graph of funtion shown below. (1+1+2 Marks) (a) Draw the graph of y = 2 on the same axis. (b) Use the graph to find (0) The values of of x when 6x2 - 2x - 3 = 2 Find the cordinate of the vertex (1) Find the equation of the axis of symetry.
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
(2 points) Here are several points on the complex plane: The red point represents the complex number zı = and the blue point represents the complex number Z2 = The "modulus" of a complex number z = x+iy, written [z], is the distance of that number from the origin: z) = x2 + y2. Find the modulus of zi. |zıl = 61^(1/2) We can also write a complex number z in polar coordinates (r, 6). The angle is sometimes called...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
how do I find the x intercepts in part b?
1. (20 marks, Sec. 1.3) Let f and g be linear functions with equations f(x) mi+b and g(r)mb (a) Is the composition f o g a linear function? If so, what is the slope and y-intercept of its graph? (bIs the product f g a linear function? If not, what type of function is it? What are the r-intercepts?
QUESTION
6
[10
marks]
F
or the circuit below,
a) [5 marks] Fin
d the current phasor
I
x
using superposition.
b) [3 marks] Verify your answer in part a) using nodal or mesh
analysis.
c) [2 marks] Gi
ven the frequency
!
=
2
!"#
/
!"#
,
write
the corresponding
values for elements
R, L, C, and
the
expressions for source
s
v
x
(t)
and
i
y
(t)
on the diagram below.
QUESTION 7 [10 marks] For...
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch the region. 5x2-2. f(x)--3x2 + 30 and g(x) marks) c) Evaluate the following integrals. Give your answers to 2 decimal places. dac i) 2 (3+2 dx. (8 marks) [25 marks]
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch...
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