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PROBLEM 2 Consider the family of circles P = {C, TER>0}, where Cr = {(x, y)...
Problem 10.13. Recal that a polynomial p over R is an expression of the form p(x) an"+an--+..+ar +ao where each aj E R and n E N. The largest integer j such that a/ 0 is the degree of p. We d...
Problem 10.13. Recal that a polynomial p over R is an expression of the form p(x) an"+an--+..+ar +ao where each aj E R and n E N. The largest integer j such that a/ 0 is the degree of p. We define the degree of the constant polynomial p0 to be -. (A polynomial over R defines a function p : R R.) (a) Define a relation on the set of polynomials by p if and only if p(0) (0)...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra...
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra f, are continuous, is A(S) = SVGC3. y)]? + [f;(x, y)]? +T dA If you attempt to use Formula 2 to find the area of the top half of the sphere x + y2 + 2? = a, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle...
5. Let F(x, y, z) = (yz, xz, xy) and define Cr,h = {(x, y, z)...
5. Let F(x, y, z) = (yz, xz, xy) and define Cr,h = {(x, y, z) : x2 + y2 = p2, z = h}. 1 Show that for any r > 0 and h ER, Sony F. dx = 0
5. Solve the initial-value problem associated with the linear first-order ODE z y + * In(x)...
5. Solve the initial-value problem associated with the linear first-order ODE z y + * In(x) y = 2e3x y(1) = 0, O O where the prime stands for differentiation with respect to x. O A. y = r-> (3x + Ke"), where K is an arbitrary constant. B.y=r" (e3+ Ke*), where K is an arbitrary constant. C.y=r-(+2 – 23). OD. y = x* (032 – *+2). O E. y = x-P(.38 – 42+2). OE y = x? (032 –...
Evaluate ∫∫∫ E √ x 2 + y 2 + z 2 d V where E...
Evaluate
∫∫∫
E
√
x
2
+
y
2
+
z
2
d
V
where
E
lies above the cone
z
=
√
x
2
+
y
2
and between the spheres
x
2
+
y
2
+
z
2
= 1
and
x
2
+
y
2
+
z
2
= 9
.
df (76 KB) 2. Evaluate r2 + y2 + 22 dV x2 + y2 and between the spheres r? + y2 + 2 = 1 and...
Evaluate the following: where S-( (z, y) є R2 : 0 ST/2,0 < y ST/2). (a)...
Evaluate the following: where S-( (z, y) є R2 : 0 ST/2,0 < y ST/2). (a) Jls (cosz-s (b) fdl where y is the line segment from (2,-1,3) to (0, 1, 4) and f (x,y,z)-y+2 sin y) dA 3 marks 3 marks (c) Jc F dr where C is the unit circle centred at the origin, traversed once anticlockwise and F R2R2 is given by F(r,y)- (x2.x + y) 3 marks JJR eVEdA where R is the region enclosed by...
Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give you...
Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give your answer in decimal form. 2 '2
Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give your...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,1,2, ..., k> 1 is an integer, 0 <P1 <1,0 <p2 <1, and p1 + P2 <1, find the marginal pmfs of X and Y and the conditional pmf of Y given X = r.
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Com...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
Problem 10.13. Recal that a polynomial p over R is an expression of the form p(x) an"+an--+..+ar +ao where each aj E R and n E N. The largest integer j such that a/ 0 is the degree of p. We define the degree of the constant polynomial p0 to be -. (A polynomial over R defines a function p : R R.) (a) Define a relation on the set of polynomials by p if and only if p(0) (0)...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra f, are continuous, is A(S) = SVGC3. y)]? + [f;(x, y)]? +T dA If you attempt to use Formula 2 to find the area of the top half of the sphere x + y2 + 2? = a, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle...
5. Let F(x, y, z) = (yz, xz, xy) and define Cr,h = {(x, y, z) : x2 + y2 = p2, z = h}. 1 Show that for any r > 0 and h ER, Sony F. dx = 0
5. Solve the initial-value problem associated with the linear first-order ODE z y + * In(x) y = 2e3x y(1) = 0, O O where the prime stands for differentiation with respect to x. O A. y = r-> (3x + Ke"), where K is an arbitrary constant. B.y=r" (e3+ Ke*), where K is an arbitrary constant. C.y=r-(+2 – 23). OD. y = x* (032 – *+2). O E. y = x-P(.38 – 42+2). OE y = x? (032 –...
Evaluate
∫∫∫
E
√
x
2
+
y
2
+
z
2
d
V
where
E
lies above the cone
z
=
√
x
2
+
y
2
and between the spheres
x
2
+
y
2
+
z
2
= 1
and
x
2
+
y
2
+
z
2
= 9
.
df (76 KB) 2. Evaluate r2 + y2 + 22 dV x2 + y2 and between the spheres r? + y2 + 2 = 1 and...
Evaluate the following: where S-( (z, y) є R2 : 0 ST/2,0 < y ST/2). (a) Jls (cosz-s (b) fdl where y is the line segment from (2,-1,3) to (0, 1, 4) and f (x,y,z)-y+2 sin y) dA 3 marks 3 marks (c) Jc F dr where C is the unit circle centred at the origin, traversed once anticlockwise and F R2R2 is given by F(r,y)- (x2.x + y) 3 marks JJR eVEdA where R is the region enclosed by...
Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give your answer in decimal form. 2 '2
Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give your...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,1,2, ..., k> 1 is an integer, 0 <P1 <1,0 <p2 <1, and p1 + P2 <1, find the marginal pmfs of X and Y and the conditional pmf of Y given X = r.
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
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